Question

For what values of λ, the vectors i - λj + 2K and 8i + 6j - k are at right angles?

Answer 1

Solution:

$\vec a=\hat i-\lambda \hat j+2\hat k\\\\\vec b=8\hat i+6\hat j-\hat k$

if both vectors are at right angles then there dot product must equal to 0.

As
$cos \: \theta = \frac{\vec a.\vec b}{ |\vec a| |\vec b| } \\ \\ cos \: 90 = \frac{8 - 6\lambda - 2}{ |\vec a| |\vec b| } \\ \\ 6 - 6\lambda = 0 \\ \\ 6\lambda=6\\\\\lambda=1$
Thus value of lambda is equal to 1 if both the vectors are perpendicular.