How do I do this Q?

[Phenotype]

The vector resolute of u in the direction of v is 3i-2j+k
The vector resolute of u perpendicular to v is 2i+xj+2k

Show that x=4



Hence find u

How do I attempt this? I forgot.

[luken93]

Let the vector resolute of u in the direction of v = Vector a
Let the vector resolute of u perpendicular to v = Vector b

Because a and b are perpendicular to eachother, a.b = 0

(a1i x b1i) + (a2j x b2j) + (a3k x b3k) = 0

(3 x 2) + (-2 x x) + (1 x 2) = 0

6 -2x + 2 = 0

-2x = -8

x = 4

[Phenotype]

but why do they use the vector set u in the direction AND perpendicular? doesn't that mean that the vector resolute of u in the direction of v = vector resolute of u perpendicular to v?

if you were to draw a triangle, wouldn't v be running as a straight line, u be a scalar multiple of v because it was parallel and u also be the vector set perpendicular to v?
why doesn't u=u?

or is it just because they used terrible/confusing wording?

could someone draw a graph for me? Am I unaware of some basic notion that V= something and U= something constantly?

[luken93]

I've attached what I've percieved the question as...

I'm not sure what you're asking, so hopefully it'll make more sense.

[Phenotype]

yeah thanks luken93, I see what I was doing wrong. Totally not in the right mindset and thinking way too complicated.
I understand now cheers

[luken93]

No worries

[Phenotype]

I have another question:

A = (1,0,5)
B = (-1,2,4)
C = (3,5,2)

Find the points of D such that ABCD is a parallelogram.

I established earlier that AB = -2i+2j-k

So |AB|=|CD| yes?

I let OD = xi+yj+zk

but eventually I just get -5=x^2 after an identical equation solve.
Can someone help?

[kamil9876]

Solving |AB|=|CD| is not sufficient because there are many points D that satisfy this and not all are such that AB is parrallel to CD (ie just take any circle of radius |AB| around C)

The best way to do this is to notice that we must have AB=DC and this is easy to solve.

[Phenotype]

Someone needs to hit me and stop overcomplicating things.

[Phenotype]

Someone needs to hit me and tell me to stop overcomplicating things.