Question

find a unit vector in the plane of vectors a=i + 2j ans b= j + 2k perpendicular to the vector c=2i+j+2k​

Answer 1

Step-by-step explanation:

Given find a unit vector in the plane of vectors a=i + 2j and b= j + 2k perpendicular to the vector c=2i+j+2k

• So given vectors are  
• vector a = i + 2j + 0k
• vector b = 0i + j + 2k
• vector c = 2i + j + 2k
• Consider
• vector a x vector b =  i           j           k
•                                   1          2          0
•                                    0          1          2
•                          = 4i – 2j + k
• (vector a x vector b ) x vector c = i       j       k
•                                                        4      -2     1
•                                                        2       1     2
•                              = - 5i – 6j + 8k
• mod (vector a x vector b ) x vector c =  (vector a x vector b) x vector c
•                               = √ (-5)^2 + (- 6)^2 + 8^2  
•                               = √25 + 36 + 64
•                                = √125
•                                   5√5
•  Now the unit vector will be 1/√5 (- 5i – 6j + 8k)

   Reference link will be

https://brainly.in/question/4717074

Answer 2

Answer:

firstly multiple vector a× vector b=( say m)

then multiple vector m × vector c

now find the unit vector

= vector m × vector c/|vector m × vector c|