Question

Given vectors a = [7, 3] and b = [-2, 2],

a) Find proj \(\bf _{b} a\) (Already found it; it's [2, -2]

b) Resolve vector 'a' in to rectangular components one of which is in the direction of vector b. (this is what i need help with)

Answer 1

@mukushla @whpalmer4 @dumbcow @kropot72

Answer 2

neat :-)

Answer 3

wats neat lol

Answer 4

Find the unit vector \(\hat b=\dfrac1{\|\vec{b}\|}\vec{b}=\dfrac1{2\sqrt2}(-2,2)=(-1/\sqrt2,1/\sqrt2)\)

Answer 5

instead of doing the steps and giving me the answer, it'd be better if u just outlined the steps required

Answer 6

Find the projection in the direction of \(\hat{b}\) -- this is exactly the component asked for in (b):$$\DeclareMathOperator{\proj}{proj}\proj\ _{\hat{b}}\vec{a}=(\vec{a}\cdot\hat{b})\hat{b}=\dots$$

Answer 7

The 'other' component is then just \(\vec{a}-\proj\ _{\hat{b}}\vec{a}\)

Answer 8

that's [2, -2]

Answer 9

so a) and b) have the same answer?