Thread: 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.

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

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

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

Hello Captain Black!

Thanks for your reply!

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

So the answers to the questions are correct?

Thanks!

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

Thanks.