vector help!

[leyva2389]

For this problem I dont know if I am to pick my own constant and vectors. I am stuck on how to even start this problem.

Let a and b be constant vectors and let c be the vector defined by the equation

c=(cost)a+(sint)b

a.) for what value(s) of t is c parallel to a?
b.) when is c parallel to b?
c.) can c ever be parallel to a+b?
d.) can c ever be perpendicular to a+b?

 

[pka]

Let a and b be constant vectors and let c be the vector defined by the equation
c=(cost)a+(sint)b
a.) for what value(s) of t is c parallel to a?
b.) when is c parallel to b?
c.) can c ever be parallel to a+b?
d.) can c ever be perpendicular to a+b?

There are many, many things to consider here.
Assume that neither \(\displaystyle \vec{a}\text{ nor }\vec{b} \) is zero.

If \(\displaystyle \vec{a}\|\vec{b} \) then a), b), c) are true period. d) is never true.

If \(\displaystyle \vec{a}\not\|\vec{b} \) (not parallel):
a) is if \(\displaystyle t=2k\pi,~k\in\mathbb{Z} \)

b) is if \(\displaystyle t=\frac{(2k+1)\pi}{2},~k\in\mathbb{Z} \)

Now, you show us some of your work on the rest of these.