Question

Determine whether the vectors u and v are parallel, orthogonal, or neither.

Answer 1

Answer:  orthogonal

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Explanation:

For any two vectors defined as follows

u = <a,b>

v = <c,d>

the dot product is computed by

u dot v = a*c + b*d

If the dot product of the vectors is 0, then the vectors are orthogonal. Meaning they are perpendicular to one another.

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Let's find the dot product of these two given vectors

u = < 2, -4 >

v = < 6, 3 >

u dot v = 2*6 + (-4)*3

u dot v = 12 - 12

u dot v = 0

Therefore, these two vectors form a right angle and are orthogonal

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Extra info:

If we can show that u = <a, b> and v = <ka, kb> for some real number k, then we have shown that vectors u and v are parallel.