Provide solution for RD Sharma Maths Class 12 Chapter 24 Vector or Cross Product exercise Very Short Answer Question, question 15.

$(\vec{a} \times \vec{b}) \cdot \vec{a}=(-\hat{\imath}+7 \hat{\jmath}+5 \hat{k}) \cdot(3 \hat{\imath}-\hat{\jmath}+2 \hat{k})$

HINT:

Find $(\vec{a} \times \vec{b})$ then

GIVEN

\begin{aligned} &\vec{a}=3 \hat{i}-\hat{j}+2 \hat{k} \\ &\vec{b}=2 \hat{i}+\hat{j}-\hat{k} \end{aligned}

SOLUTION:

\begin{aligned} &\vec{a}=3 \hat{i}-\hat{j}+2 \hat{k} \\ &\vec{b}=2 \hat{i}+\hat{j}-\hat{k} \end{aligned}

\begin{aligned} \therefore(\vec{a} \times \vec{b}) &=\left|\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ 3 & -1 & 2 \\ 2 & 1 & -1 \end{array}\right| \\ &=\hat{i}(1-2)-\hat{j}(-3-4)+\hat{k}(3+2) \\ &=-\hat{i}+7 \hat{j}+5 \hat{k} \\ (\vec{a} \times \vec{b}) \cdot \vec{a} &=(-\hat{i}+7 \hat{j}+5 \hat{k}) \cdot(3 \hat{i}-\hat{j}+2 \hat{k}) \end{aligned}

Here in question dot product is not asked so the above remains as it is.

Or we can say that it is meaningless.