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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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