Q. 184.7( 3 Votes )

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Answer :

Given that,



We need to find vector .


Let , where x, y, z be any scalars.


Now, for :







Comparing Left Hand Side and Right Hand Side, we get


From coefficient of z – y = 0 …(i)


From coefficient of -(z – x) = 1


x – z = 1 …(ii)


From coefficient of y – x = -1


x – y = 1 …(iii)


Also, for :




Since, , as and other dot multiplication is zero. We get,


x + y + z = 3 …(iv)


Now, add equations (ii) and (iii), we get


(x – z) + (x – y) = 1 + 1


x + x – y – z = 2


2x – y – z = 2 …(v)


Add equations (iv) and (v), we get


(x + y + z) + (2x – y – z) = 3 + 2


x + 2x + y – y + z – z = 5


3x = 5



Put value of x in equation (iii), we get


Equation (iii) x – y = 1






Put this value of y in equation (i), we get


Equation (i) z – y = 0




Since,


By putting the values of x, y and z, we get



Thus, we have found the vector .


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