Answer: 35/4
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Explanation:
Consider these two general vectors in R2
v = <a, b>
w = <c, d>
The dot product of them is
v dot w = a*c+b*d
If the dot product is zero, then the vectors are perpendicular, aka orthogonal.
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In this problem we have
v = <-7, -4>
w = <-5, k>
The idea is to take the dot product of these items and set the result equal to zero. Then isolate k.
v dot w = 0
(-7)*(-5) + (-4)*k = 0
35 - 4k = 0
4k = 35
k = 35/4
