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In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.

u=3,-1,2,v=-4,-6,3

Short Answer

Expert verified

The dot product is 0 and the angle is90°.

Step by step solution

01

Step 1. Given information.

The given pairs of vectors are:

u=3,-1,2,v=-4,-6,3

02

Step 2. Find the dot product.

The dot product is:u·v=u1v1+u2v2+u3v3

u=3,-1,2andv=-4,-6,3u·v=3-4+-1-6+23=-12+6+6=0

Therefore, the dot product of the given two vectors u=3,-1,2andv=-4,-6,3is 0.

03

Step 3. Find the angle between the two vectors.

The formula for the angle between the two vectors is:

cosθ=u.vuvu=3,-1,2andv=-4,-6,3u·v=0u=32+-12+229+1+4=14v=-42+-62+3216+36+9=61

Then,

cosθ=u.vuvcosθ=01461cosθ=0θ=cos-10=90°

Therefore, the angle is90°.

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