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#1 2007-05-05 16:44:37

Xx
Guest

Vectors

The triangle ABC is defined by

OA: 2
      -3

AB: 3
      4

AB*BC= 0 (the dot product)

AC is parallel to 0
                        1

What is BC and the vector OC?

Thanks a lot!

#2 2007-05-05 16:55:07

Xx
Guest

Re: Vectors

Oh, and one more question. The vectors i and j are unit vectors along the x- and y-axes respectively. THe vectors u = -i + 2j and v=3i+5j are given.

A vectors w has the same direction as u=-1+2j and has a magnitude of 26.
Find w in terms of i and j


THankss!

#3 2007-05-06 00:05:11

HallsofIvy
Guest

Re: Vectors

Xx wrote:

The triangle ABC is defined by

OA: 2
      -3

AB: 3
      4

AB*BC= 0 (the dot product)

AC is parallel to 0
                        1

What is BC and the vector OC?

Thanks a lot!

It would help a lot if you would write out the entire problem.  I assume that O is the origin of some coordinate system and the vector OA is <2, -3> and AB is <3, 4> .  That means that OB= <2, -3>+ <3, 4>= <5, 1> .  Specifically, in this coordianate system, A is the point (2, -3) and B is the point (5, 1).  BC is perpendicular to AB (because their dot product is 0) and C is directly above A (because AC is parallel to <0, 1>).  C must be the point (2, y) for some y.   There are now a number of ways to determine the point C.  For example, since ABC is a right triangle with right angle at B, we could use the Pythagorean theorem: the length of the hypotenuse, AC is y+ 3 and its square must equal the square of the distances from A to B and from B to C- that is math](y+3)^2= 25+ 9+ (y-1)^2[/math].  That should be easy to solve.

  Even simpler is to use symmetry.  Since AB is <3, 4> and BC is perpendicular to it (and C is above A), BC must be <-4, 3>.  Then C is the point (5-4,1+3)= (1, 4) and OC is <1, 4>.

#4 2007-05-06 00:07:16

HallsofIvy
Guest

Re: Vectors

Xx wrote:

Oh, and one more question. The vectors i and j are unit vectors along the x- and y-axes respectively. THe vectors u = -i + 2j and v=3i+5j are given.

A vectors w has the same direction as u=-1+2j and has a magnitude of 26.
Find w in terms of i and j


THankss!

This is easier than the first problem.  u has length

.  Divide each component by
to get a unit vector in that direction and then multiply by 26 to get a vector with magnitude 26 in that direction.

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