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.
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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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