Question

let a=2i+3j+k,b=4i+jandc=i-3j-7k. Find the vector r such that r.a=9,r.b=7andr.c=6​

Answer 1

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

r.a=9,  r.b=7  and   r.c=6​

To Find : Vector r

Solution:

Let say r = ( xi + yj + zk)

a=2i+3j+k

 r.a=9

=> 2x  + 3y  + z = 9

a=4i+j

 r.b=7

=> 4x  +  y   = 7

c=i-3j-7k

 r.c=6

=>  x  - 3y  - 7z = 6

2x  + 3y  + z = 9    Eq1

4x  +  y   = 7          Eq2

x  - 3y  - 7z = 6     Eq3

7*Eq1 + Eq3

=>  15x + 18y = 69

=> 5x + 6y = 23

4x  +  y   = 7   => 24x  + 6y  = 42

=> 19x = 19

=> x = 1

=> y = 3

2x  + 3y  + z = 9

=> 2 + 9 + z = 9

=> z  = - 2

r = (i + 3j - 2k)

r = (i + 3j - 2k)

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