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Chapter 9: Q. 36 (page 627)

Use the given vectors u, v, and w to find each expression.

u=2i-3j+k,v=-3i+3j+2k,w=i+j+3k(u脳v).w

Short Answer

Expert verified

The required value of the expression is-25.

Step by step solution

01

Step 1. Given Information  

We are given three vectors u,v,w and we need to find the cross product of (u脳v).w.

02

Step 2. Finding cross product  

u=2i-3j+kv=-3i+3j+2kw=i+j+3k

The required cross product is

u脳v=ijk2-31-332=i-3132-j21-32+k2-3-33=i((-3).2-3.1)-j(2.2-(-3).1)+k(2.3-(-3).(-3))=-9i-7j-3k

03

Step 3. Finding dot product   

The required dot product is

(u脳v).w=(-9i-7j-3k).(i+j+3k)=(-9).1+(-7).1+(-3).3=-9-7-9=-25

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