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

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

Answers (1)

ANSWER:

(\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.

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