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Prove Theorem 10.11; that is, show that when v0, the scaled vector role="math" localid="1663644167280" 1vv is a unit vector with the same direction as v.

Short Answer

Expert verified

It is proven that,1vvis a unit vector with the same direction asv.

Step by step solution

01

Consider a vector

Let us consider that,

v=i+j+k

02

Proof

Now calculate the magnitude of vector v,

v=12+12+12=1+1+1=3

The scaled vector 1vvis,

1vv=13i+j+k=13i+13j+13k

The magnitude of the scaled vector 1vvis computed as,

1vv=132+132+132=13+13+13=33=1=1

Since the magnitude of the scaled vector is unity.

Therefore, the scaled vector is a unit vector.

Hence, proved.

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