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Chapter 9: Q. 19 (page 627)

find (a) v 脳 w, (b) w 脳 v, (c) w 脳 w, and

(d) v 脳 v

v = 2i - j + 2k

w = j - k

Short Answer

Expert verified

v 脳w= -i +2j +2k

w 脳v= i -2j -2k

w 脳w=0

v 脳v=0

Step by step solution

01

Step 1. Given Information

v = 2i - j + 2k

w = j - k

02

Step 2. Cross product  v× w  

For two vectors

v=a1i+b1j+c1k

w=a2i+b2j+c2k

cross product v脳 w is written as

v = 2i - j + 2k

w = j - k


v脳w=ijk2-1201-1=i-121-1-j220-1+k2-101=-i+2j+2k

03

Step 3. w × v 

According to the algebraic properties of cross product

w 脳 v = -(v 脳 w)

so w 脳 v=-(-i+2j+2k) = i -2j -2k

04

Step 4. w× w and v× v 

According to the algebraic properties of cross product the cross product of any vector with itself is the zero vector

(a 脳a=0).

Hence w 脳w=0 and v 脳v=0

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