Question

if A =7i^+2j^-3k is parellel to B=14i+4j+ak then value of a will be​

Answer 1

Given : A =7i^+2j^-3k is parallel  to B=14i+4j+ak

To Find : Value of a

Solution:

A =7i^+2j^-3k

B=14i+4j+ak

Parallel if

7/14  = 2/4  = -3/a

=> 1/2 = 1/2 = -3/a

=> a = - 6

Another method :

Since given two vectors are parallel

$\displaystyle\begin{vmatrix} \hat{ \imath} & \hat{ \jmath} & \hat{k}\\ 7 & 2 & - 3 \\ 14 & 4 & a \end{vmatrix} = \hat{0}$

=> i^(2a + 12)  + j^(7a + 42) + k(28-28) = 0

=> i^(2(a + 6))  + j^(7(a + 6)) + k(28-28) = 0

=>2(a + 6) = 0

=> a  + 6  0

=> a = - 6

or

7(a + 6) = 0

=>  a + 6 = 0

=> a = - 6

Value of a = -6

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