Mathematics - Vector Question with Solution | TestHub

$\begin{array}{rl}& {\overline{\mathrm{a}}}_1=\lambda \hat{\mathrm{i}}+2\hat{\mathrm{j}}+\hat{\mathrm{k}}\\ & {\overline{\mathrm{a}}}_2=-2\hat{\mathrm{i}}-5\hat{\mathrm{j}}+4\hat{\mathrm{k}}\\ & \overrightarrow{\mathrm{p}}-=3\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}\\ & \overrightarrow{\mathrm{q}}-=-3\hat{\mathrm{i}}+2\hat{\mathrm{j}}+4\hat{\mathrm{k}}\\ & (\lambda +2)\hat{\mathrm{i}}+7\hat{\mathrm{j}}-3\hat{\mathrm{k}}={\overline{\mathrm{a}}}_1-{\overline{\mathrm{a}}}_2\\ & \overrightarrow{\mathrm{p}}\times \overrightarrow{\mathrm{q}}-=-6\hat{\mathrm{i}}-15\hat{\mathrm{j}}+3\hat{\mathrm{k}}\end{array}$
$\begin{array}{rl}& \frac{44}{\sqrt{30}}=\frac{|-6\lambda -12-105-9|}{\sqrt{(-6{)}^2+(-15{)}^2+3^2}}\\ & \frac{44}{\sqrt{30}}=\frac{|6\lambda +126|}{3\sqrt{30}}\\ & 132=|6\lambda +126|\\ & \lambda =1,\lambda =-43\\ & |\lambda |=43\end{array}$