Math Is Fun Forum

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Equation

Question 1Equation of line parallel to x+3y-9=0 is??

Question 2 The angle between vectors 2i+3j+k and 2i-j-k is
tell how to find an angle between vectorrs

Last edited by Zeeshan 01 (2017-04-24 21:12:52)

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Equation

Hi;

There are lots of lines parallel to that one. Start by finding the slope. You do that by putting the equation into standard form y = mx + b

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Equation

Ok I find slope that is -1÷3 how put in y=mx+c I have no y intercept

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Equation

Hi;

That is the correct slope. Did you solve for y in the equation x+3y-9=0? Then you can get the y intercept.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Equation

Did you solve for y in the equation x+3y-9=0? Then you can get the y intercept.
X=0??? And why use slope intercept form???

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Equation

I have no y intercept

Do you need the y intercept or not?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Equation

Yes need !!!

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Equation

The y intercept is where x = 0. So plug in in x = 0 in x+3y-9=0 and solve for y.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Equation

Ok get the ans of question 1 but why we use slope intercept form??

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Equation

We did not use the slope intercept form. We are still plugging x = 0 into x+3y-9=0 to get the y intercept.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Equation

I solve In my copy it's ans same as question but it is wrong

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Malik

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Equation

Question 2 The angle between vectors 2i+3j+k and 2i-j-k is ???? And

tell how to find an angle between vectorrs

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Equation

hi Zeeshan 01

You can make an equation for this using the 'scalar' or 'dot' product.  Do you what a scalar product is?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

tanith

Member

Registered: 2017-04-26

Posts: 9

Re: Equation

The angle between two n-dimensional vectors u and v can be calculated by using

Suppose we have two vectors

We can use the above formula to calculate the angle.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Equation

Look formula please a · b = |a| × |b| × cos(θ)
https://www.mathsisfun.com/algebra/vectors-dot-product.html

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Equation

It is the same formula.  tanith has re-arranged it to make the angle the subject to make it easier for you.

Note also: it is called the 'dot' product because a 'dot' is used rather than a times sign.  It's best to stick to this because {vector 1} x {vector 2} means use the 'vector' product which is a very different thing.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Equation

Why we not use sin of angle theta ??

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Equation

hi Zeeshan 01

The scalar product is defined that way.  It is useful because the cosine of a vector gives the component of that vector in a certain direction.  So the scalar product can be used to determine

eg1.  Magnetic flux is the dot product of the magnetic field and the area vectors.
eg2. Work done by a force is F.d where the Force is F, and d is the vector for the distance moved.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Equation

Question 1Equation of line parallel to x+3y-9=0 is??
Can you see this question when I use slope and y intercept ans is same as question????

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Equation

hi Zeeshan 01

In that line the 1 in 1x and the 3 in 3y completely determine the slope of the line.  The -9 only affects where the line crosses the axes.

As a parallel line must have the same slope,  any of the following will be parallel:

x + 3y + 10 = 0
x + 3y +100 = 0
x + 3y = 97

even

2x + 6y + 17 = 0 because the ratio is still 2:6 = 1:3

So these will also work:

2x + 6y + 100 = 0
12x + 36y - 1000 = 0

even

0.5x + 1.5y + 1.23456 = 0

You just have to make sure that in the equation ax + by + c = 0,      a:b = 1:3

So, there plenty to choose from (an infinite number as there's an infinite number of parallel lines).  Just make sure you don't accidentally pick the same line as the question:

eg.  2x + 6y - 18 = 0 is just the question line doubled.

Please make up one of your own rather than pick one of mine.  That will show you have understood.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Equation

Can you tell about how to take ratio???

How u take those LINES? ??

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Equation

Let us try to follow the numbers as an equation is re-arranged.

The slope is -a/b

Any line parallel must have the same slope, -a/b

You could do this:

Example Find a line parallel to 3x + 5y - 7 = 0

The slope is -3/5 so I'll make up a new line with the same slope:

Please notice that the ratio 3:5 appears all the way through this problem.  Once you realise this will always happen, you don't need to make the slope intercept form to answer the question.  It is easy to write answers down just by using 3 and 5. 

Like this.  Here are some more possible answers:

3x + 5y -12 = 0
3x + 5y + 100 = 0
6x + 10y + 20 = 0 [because this is the same as 3x + 5y + 10 = 0]
300x + 500y + 10000 = 0
.......................
.......................

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Equation

Good answer Thanks I Understand!!

We can find many parallel lines if we want by using SLOPE? ??

How much importance did slope play...??!!!!

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Equation

Zeeshan 01

How much importance did slope play...??!!!!

If you want two lines to be parallel on a graph, then slope is everything!

In this diagram AC and BE are parallel lines.  ABD is a vertical line, and both BC and DE are horizontal.

The slope of line AC is AB/CB.

The slope of BE is BD/ED.

The triangles ABC and BDE are similar because AC // BE ; AB // BD ; and BC // DE so all three angles of one triangle are equal to the equivalent angles in the other triangle.  // is an abbreviation for 'is parallel to' .

If the two triangles are similar then their corresponding sides are in the same ratio

So parallel lines have the same slope values.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Equation

What about perpendicular??? How u draw IT? ?

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Malik