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Chapter 10: Q .8. (page 811)

What is the relationship between鈥�v鈥�andv路v?

Short Answer

Expert verified

鈥�v鈥�andv路vare related as followsv路v=鈥�v鈥�2

Step by step solution

01

Step 1:Given information

鈥�v鈥�andv路v

02

Step 2:Simplification

Consider the vector鈥�v鈥�andv路v.

Ifuandvare the vector such thatu=u1,u2,u3andv=v1,v2,v3, then dot product is given

byu.v=u1v1+u2v2+w1w2.

NOW,v=v1,v2,v3

Therefore,

V.V=v1路v1+v2路v2+v3路v3

=v12+v22+v22

Therefore, the dot product of the two vectors v.v isv12+v22+v22

Ifvis the vector inR3such thatv=v1,v2,v3, then norm of the vector is given by

鈥�v鈥�=v12+v22+v32

From (1) and (2) it is clear that

V路V=鈥�V鈥�2

Hence,鈥�v鈥�andv路vare related as followsv路v=鈥�v鈥�2

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Most popular questions from this chapter

If u, v and w are three vectors in 鈩�3, which of the following products make sense and which do not?

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