Correct answer is 43
\(\bar{a}_{1}=\lambda \hat{i}+2 \hat{j}+\hat{k}\)
\(\bar{a}_{2}=-2 \hat{i}-5 \hat{j}+4 \hat{k}\)
\(\overrightarrow{\mathrm{p}}-=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}\)
\(\vec{q}-=-3 \hat{i}+2 \hat{j}+4 \hat{k}\)
\((\lambda+2) \hat{i}+7 \hat{j}-3 \hat{k}=\bar{a}_{1}-\bar{a}_{2}\)
\(\overrightarrow{\mathrm{p}} \times \overrightarrow{\mathrm{q}}-=-6 \hat{\mathrm{i}}-15 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\)
\(\frac{44}{\sqrt{30}}=\frac{|-6 \lambda-12-105-9|}{\sqrt{(-6)^2+(-15)^2+3^2}}\)
\(\frac{44}{\sqrt{30}}=\frac{|6 \lambda+126|}{3 \sqrt{30}}\)
\(132=|6 \lambda+126|\)
\(\lambda=1, \lambda=-43\)
\(| \lambda|=43\)
