Find b41 such that a and b are orthogonal. a=(2 0 -1 3) b=(6 -1 3 b41)
Question
Find b41 such that a and b are orthogonal. a=(2 0 -1 3) b=(6 -1 3 b41)
Solution
Two vectors are orthogonal if their dot product is zero. The dot product of vectors a and b is calculated as follows:
a.b = (26) + (0-1) + (-13) + (3b41) = 0
This simplifies to:
12 - 3 + 3*b41 = 0
Further simplifying gives:
9 + 3*b41 = 0
Solving for b41 gives:
3*b41 = -9
b41 = -9 / 3
b41 = -3
So, the value of b41 that makes vectors a and b orthogonal is -3.
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