asked 214k views
2 votes
Which of the following vectors are orthogonal to (-1,3)?

A. (-6,-2)
B. (-2,-3)
C. (1,3)
D. (3,1)

asked
User Tirdadc
by
8.3k points

2 Answers

6 votes

Answer:

A. (-6,-2) D. (3,1)

Explanation:

Just did it on A p e x

3 votes
Any vector that is a multiple of (3, 1) will be orthogonal. These include
.. A (-6, -2)
.. D (3, 1)

_____
The dot-product of these with (-1, 3) is zero:
(-6*-1 +-2*3) = 6 -6 = 0
(3*-1 +1*3) = -3 +3 = 0

You can make a vector orthogonal to a 2-D vector by swapping the coordinates and negating one of them. When you swap the elements of (-1, 3) you get (3, -1). It is usually convenient to negate the one that is already negative, so that would give you (3, 1) as the orthogonal vector.
answered
User Joshua Burgner
by
7.5k points
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