Question

Find the scaler component of a unit vector which is perpendicular to vectors i+2j-k and 3i-j+2k.

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

$\rm \: \vec{a} = \hat{i} + 2\hat{j} - \hat{k}$

and

$\rm \: \vec{b} = 3\hat{i} - \hat{j} + 2\hat{k}$

Now, Consider

$\red{\sf \: \vec{a} \times \vec{b}}$

$\rm \: = \: \: \: \begin{gathered}\sf \left | \begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\1&2& - 1\\3& - 1& 2\end{array}\right | \end{gathered}$

$\rm \: = \: \hat{i}(4 - 1) - \hat{j}(2 + 3) + \hat{k}( - 1 - 6)$

[ Please see the attachment onwards this ]