Question

Find $\lambda$ and $\mu$ if $(\hat{i}+3\hat{j}+9k)\times (3\hat{i}-\lambda \hat{j}+\mu k)=0.$

Answer 1

Given $(i+3j+9k)\times (3i-\lambda j+\mu k)=0$

Now we should do cross product of two given vectors and equate it to zero
$\left|\begin{array}{ccc}i& j& k\\ 1& 3& 9\\ 3& -\lambda & \mu \end{array}\right|$

$=i(3\mu +9\lambda )+j(27-\mu )+k(-\lambda -9)=0$

Hence, 3$\mu$ + 9$\lambda$$=0$

$27$ - $\mu$$=0$

-$\lambda$$-9=0$

Solving above three equstions, we get, $\mu =27$ , $\lambda =-9.$