Question

if a=2i+j-k, b=4i-7j+k, find a vector c such that axc=b and a.c=6

Answer 1

let vector C be like ai+ bj +ck
find a×c
then a.c
to know values of a,b,c

Answer 2

let the vector c=xi+yj+zk.

axc=

         $\left[\begin{array}{ccc}i&j&k\\2&1&-1\\x&y&z\end{array}\right]$

=i(z-+y)-j(2z+x)+k(2y-x)                      

b=4i-7j+k

now equate axc and b vectors in i,j and k:

i: z+y=4   ⇒y=4-z                            Equation 1

j: 2z+x=7 ⇒x=7-2z                          Equation 2

k: 2y-x=1

and a.c=(2i+j-k).(xi+yj+zk)=6

      2x+y-z=6                                 Equation 3

Solve the above equations by putting 1 and 2 in equation 3:

⇒2(7-2z)+(4-z)-z=6

⇒14-4z+4-z-z=6

⇒12=6z

⇒z=2

 x=7-2z=7-2(2)=3

 y=4-z=4-2=2

∴c=3i+2j+2k