1. ## Vector problems

Vector Calculations

Hello all. Need to verify some answers to questions i've completed.

Given the vectors v = (1,0,1) and w = (-1,1,2)

i) Find the vector projections of w onto v.

My solution: I used the formula (w . unit vector of v) * unit vector of v

unit vector of v is equal to 1 / (root 2) * (1,0,1)
so then (-1,1,2) . (1/ (root 2), 0, 1 / (root 2)) = ( 1/ (root 2) + 0 + 2 / (root 2)) = 1 / (root 2)

I multiplied 1 / (root 2) by the unit vector of v to get (1/2, 0, 1/2) as the vector projection of w onto v.

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ii) Find the projection of w orthagonal to v

My solution: v perpendicular = w - projection of w onto v = (-1,1,2) - (1/2, 0, 1/2) which gave me an answer of (-3/2, 1, 1/2).

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iii) Find the area of the parallelogram spanned by the vectors v and w. (Note: this question means to ask the area of the parallelogram whose sides are given by vectors v and w)

My Solution: For this question i simply found the lengths of v (root 6) and w (root 2) and multiplied them together to get an answer of 2 (root 3).

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2.) Sketch 4y^2 + 9x^2 + 16y - 18x - 11 = 0

My solution: I won't show the full working because it is too long, but i used basic algebra and completing the square to yield: (y+4)^2 / 9 + (x-1)^2 / 4 = 1

this is the basic form of an elipse graph so,

I set x = +1 and got y = -1, -7 (the y-vertices of the elipse)
and I set y = -4 and got x = 3, -1 (the x-vertices of the ellipse)

The centre of the elipse is at (1,-4)

a is greater than b so the major axis is parallel to x-axis.

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Thanks guys.

2. ## Re: Vector problems

Originally Posted by andrew2322
Given the vectors v = (1,0,1) and w = (-1,1,2)[/B]
i) Find the vector projections of w onto v.
ii) Find the projection of w orthagonal to v
First please learn to use LaTeX.
If that is too much for you, the please do no use special fonts!
The $\text{proj}_vw=\frac{v\cdot w}{v\cdot v}v$

3. ## Re: Vector problems

hello, sorry for the duplicate post. Plato, could you please check my answers for me? i will master latex by this week!

4. ## Re: Vector problems

$1/4$

5. ## Re: Vector problems

Originally Posted by andrew2322
Vector Calculations

Hello all. Need to verify some answers to questions i've completed.

Given the vectors v = (1,0,1) and w = (-1,1,2)

i) Find the vector projections of w onto v.

My solution: I used the formula (w . unit vector of v) * unit vector of v

unit vector of v is equal to 1 / (root 2) * (1,0,1)
so then (-1,1,2) . (1/ (root 2), 0, 1 / (root 2)) = ( 1/ (root 2) + 0 + 2 / (root 2)) = 1 / (root 2)

I multiplied 1 / (root 2) by the unit vector of v to get (1/2, 0, 1/2) as the vector projection of w onto v.

It is going around the houses a bit (see Plato's post) but correct.

CB

6. ## Re: Vector problems

Hello Captain Black!

I'm not sure what is meant by 'going around the house'?

So the answers to the questions are correct?

Thanks!

7. ## Re: Vector problems

Sorry, you only quoted the first part of the questions. Are the rest also correct?

Thanks.