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discy
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Homework Statement
Vectors
find k if (4,1,k)τ & (5,1,-3)τ are perpendicular?
From the answer sheet I know the answer is k = 7
Homework Equations
I believe I need these two but I'm not certain:
Dot-product: v*w = v1w1 + v2w2 + ... vdwd
cos θ = v*w / ||v|| * ||w||
The Attempt at a Solution
[STRIKE]Because θ = arccos(v*w / ||v|| * ||w||) = the angle between two vectors. θ should be 90 = perpendicular.
90 = arccos ((4 * 5 + 1 * 1 + k * -3) / √(4²+1²+k²) * √(5²+1²+(-3)²)) =
90 = arccos (21-3k / √(17+k²) * √35)
90 = arccos(21-3k / √(17+k²) * √35)[/STRIKE]
cos(90) = 0 = perpendicular
[itex]\frac{21-3k}{\sqrt{17+k²} * \sqrt{35}} = 0[/itex]
what would be the easiest way to get to k = 7 ?
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