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Chapter 10: Q. 31 (page 824)

In Exercises 30鈥�35 compute the indicated quantities when u=(鈭�3,1,鈭�4),v=(2,0,5),andw=(1,3,13)

u脳wandw脳u

Short Answer

Expert verified

The value of u脳w=25i-35j-10kandw脳u=-25i+35j+10k

Step by step solution

01

Step 1. Given Information 

The indicated quantities when u=(鈭�3,1,鈭�4),v=(2,0,5),andw=(1,3,13)

We have to find the value ofu脳wandw脳u

02

Step 2. Firstly finding the value of u×w

The value of vectorsu=(鈭�3,1,鈭�4)andw=(1,3,13)

The cross product of

u脳w=detijk-31-41313

03

Step 3. Now solving the matrix.

u脳w=detijk-31-41313u脳w=((1)(13)鈭�(鈭�4)(3))i+((-3)(13)鈭�(-4)(1))j+((-3)(3)鈭�(1)(1))ku脳w=(13+12)i+(-39+4)j+(-9-1)ku脳w=25i-35j-10k

04

Step 4. Now finding the value of w×u

The value of vectorsu=(鈭�3,1,鈭�4)andw=(1,3,13)

The cross product of

w脳u=detijk1313-31-4

05

Step 5. Now solving the matrix.

w脳u=detijk1313-31-4w脳u=((鈭�4)(3)鈭�(1)(13))i+((-4)(1)-(-3)(13))j+((1)(1)-(-3)(3))kw脳u=(-12-13)i+(-4+39)j+(1+9)kw脳u=-25i+35j+10k

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