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In Exercises 22–29 compute the indicated quantities when u=(2,1,3),v=(4,0,1),andw=(2,6,5)

u×vandv×u

Short Answer

Expert verified

The value of u×v=1i+14j-4kandlocalid="1649397999598" v×u=-1i-14j+4k

Step by step solution

01

Step 1. Given Information 

In Exercises 22–29 compute the indicated quantities whenu=(2,1,3),v=(4,0,1),andw=(2,6,5)

We have to find the value ofu×vandv×u

02

Step 2. Firstly finding the value of u×v

The value of vectors u=(2,1,3),v=(4,0,1)

The cross product of u×v

localid="1649398046712" u×v=detijk21-3401

03

Step 3. Now solving the matrix.

u×v=detijk21-3401u×v=((1)(1)(-3)(0))i+((2)(1)(-3)(4))j+((2)(0)(1)(4))ku×v=(1+0)i+(2+12)j+(04)ku×v=1i+14j-4k

04

Step 4. Now finding the value of v×u

The value of vectorsu=(2,1,3),v=(4,0,1)

The cross product ofv×u=detijk40121-3

05

Step 5. Now solving the matrix. 

v×u=detijk40121-3v×u=((0)(-3)(1)(1))i+((4)(-3)(1)(2))j+((4)(1)(0)(2))kv×u=(0-1)i+(-12-2)j+(40)kv×u=-1i-14j+4k

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