Vector Question - u = u1+u2 where u1 is parallel

[EternusVia]

Homework Statement

Let u = i - 2j, v = 2i + 3j, and w = i + j. Write u = u1 + u2 where u1 is parallel to v and u2 is parallel to w. (See question 41.)

Homework Equations

Properties of vectors. Question 41: https://answers.yahoo.com/question/index?qid=20090923151849AARqpWR

The Attempt at a Solution

I haven't had much of an attempt at this because I don't how to determine analytically if a vector is parallel to another vector. Through google I found that a vector A is parallel to a vector B if their dot product, A dot B, equals 0. But this question comes immediately before the Dot Product section of my calculus textbook, so I'm assuming there's a way to figure it out using other methods.

I'd appreciate any advice pointing me towards the right v/|v|... (get it?)

Thanks

 

[LCKurtz]

Homework Statement

Let u = i - 2j, v = 2i + 3j, and w = i + j. Write u = u1 + u2 where u1 is parallel to v and u2 is parallel to w. (See question 41.)

Homework Equations

Properties of vectors. Question 41: https://answers.yahoo.com/question/index?qid=20090923151849AARqpWR

The Attempt at a Solution

I haven't had much of an attempt at this because I don't how to determine analytically if a vector is parallel to another vector.

The easy test for parallel is one vector is a multiple of the other.

Through google I found that a vector A is parallel to a vector B if their dot product, A dot B, equals 0.

No, that is the test for two vectors to be perpendicular.

But this question comes immediately before the Dot Product section of my calculus textbook, so I'm assuming there's a way to figure it out using other methods.

I'd appreciate any advice pointing me towards the right v/|v|... (get it?)

Thanks

 

[EternusVia]

No, that is the test for two vectors to be perpendicular.

You're correct. I meant to say that if the cross product equals 0, then they are parallel. http://mathworld.wolfram.com/ParallelVectors.html


But onto what you said. So a vector A is parallel to a vector B if, say, A = i + j and B = 2i + 2j?

Thanks

 

[ehild]

So a vector A is parallel to a vector B if, say, A = i + j and B = 2i + 2j?

Yes, a vector A is parallel with vector B if B=kA , with k a scalar.

ehild

 

[HallsofIvy]

Basically this problem asks you to find numbers, a and b, such that u= av+ bw. That is, such that
1- 2j= a(2i+ 3j)+ b(i+ j). You have to solve two equations in two unknowns.

 

[EternusVia]

Much to my chagrin I haven't had any luck with this problem. Would someone be able to give a brief work through or perhaps continue leading me in the right direction? It's probably so easy that a small hint would almost give the problem away...

Thanks

 

[LCKurtz]

Basically this problem asks you to find numbers, a and b, such that u= av+ bw. That is, such that
i- 2j= a(2i+ 3j)+ b(i+ j). You have to solve two equations in two unknowns.

Much to my chagrin I haven't had any luck with this problem. Would someone be able to give a brief work through or perhaps continue leading me in the right direction? It's probably so easy that a small hint would almost give the problem away...

Thanks

Show us what happened when you tried HallsOfIvy's suggestion in post #5.