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Chapter 9: Q. 36 (page 613)

If vis a unit vector and the angle between vand iis 伪,show thatv=cos伪i+sin伪j.

Short Answer

Expert verified

It is proved thatv=肠辞蝉伪i+蝉颈苍伪j.

Step by step solution

01

Step 1. Given Information

It is given that v is a unit vector and the angle between v and iis 伪.

We have to show thatv=肠辞蝉伪i+蝉颈苍伪j.

02

Step 2. Showing

It is given that vis a unit vector. Therefore, v=1.

The angle between unit vector vand iis 伪.

To show v=肠辞蝉伪i+蝉颈苍伪j let's write vin terms of components.

So,

x-component is role="math" localid="1646829085958" v=v肠辞蝉伪i

y-component is v=v蝉颈苍伪j

Thus,

v=v肠辞蝉伪i+v蝉颈苍伪jv=肠辞蝉伪i+蝉颈苍伪j

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