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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=2,0,-5,v=-3,7,-1

Short Answer

Expert verified

The dot product is-1 and the angle isrole="math" localid="1649664356753" cos-1-11711.

Step by step solution

01

Step 1. Given information.

The given pairs of vectors are:

u=2,0,-5andv=-3,7,-1

02

Step 2. Find the dot product.

The dot product is: u·v=u1v1+u2v2+u3v3

u=2,0,-5andv=-3,7,-1=2-3+07+-5-1=-6+0+5=-1

Therefore, the dot product of the given two vectors u=2,0,-5andv=-3,7,-1is-1.

03

Step 3. Find the angle between the two vectors.

The formula for the angle between the two vectors is:

cosθ=u·vuv

u=2,0,-5andv=-3,7,-1u·v=-1u=22+02+-524+0+25=29v=-32+72+-129+49+1=59

Then,

role="math" localid="1649664305708" cosθ=u·vuvcosθ=-12959θ=cos-1-11711

Therefore, the angle isrole="math" localid="1649664318896" cos-1-11711.

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