Question

let a= 2i+k, b= i+j+k, c= 4i-3j+7k, be three vectors. find a vector r which satisfies r*b=c*b and r.a=0.


how to solve this problem​

Answer 1

Given : a= 2i+k, b= i+j+k, c= 4i-3j+7k,

To Find : vector r which satisfies r*b=c*b and r.a=0.

Solution:

a= 2i+k, b= i+j+k, c= 4i-3j+7k

r =  xi + yj + zk

r.a=0

=> 2x + 0 + z  = 0

=> 2x + z  = 0

r*b=c*b

=> x + y + z  = 4 - 3 + 7

=> x + y + z  = 8

2x + z  = 0

x + y + z  = 8

=>  - x  + y  = 8

=> y = x   + 8

 y = x   + 8

z  =   - 2x

Two Equation 3 Variables

Can not be solved for unique  solution  

x = 0  , y  =  8  , z  = 0

x = 1   , y = 9   , z  = - 2

x = 2   y = 10    z = - 4  

Put any value of x and get values of y &  z

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