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  • Provide Solution for RD Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise Very Short Answer Question 19

Provide Solution for RD Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise Very Short Answer Question 19

Answers (1)

ANSWER:-  \vec{a}

GIVEN:  \vec{a}  is any vector and  (\vec{a} \hat{i}) \hat{i}+(\vec{a} \cdot \hat{j}) \hat{j}+(\vec{a} \cdot \hat{k}) \hat{k}

HINTS: you must know about the general form of any vector

SOLUTION:we know the general form of any vector.

\therefore \vec{a}=\hat{x i}+y \hat{j}+z \hat{k}\cdot \cdot \cdot \cdot (i)

Now

\begin{aligned} &(\vec{a} \hat{i}) \hat{i}+(\vec{a} \cdot \hat{j}) \hat{j}+(\vec{a} \cdot \hat{k}) \hat{k}=[x \hat{i}+y \hat{j}+z \hat{k}]\cdot \hat{i}+[x \hat{i}+y \hat{j}+z \hat{k}]\cdot \hat{j}+[\hat{x} \hat{i}+y \hat{j}+z \hat{k}] \cdot \hat{k} \\ & \end{aligned}

(\vec{a} \hat{i}) \hat{i}+(\vec{a} \cdot \hat{j}) \hat{j}+(\vec{a} \cdot \hat{k}) \hat{k}=(x+0+0) \cdot \hat{i}+(0+y+0) \cdot \hat{j}+(0+0+z) \cdot \hat{k}

\begin{aligned} &(\vec{a} \cdot \hat{i}) \hat{i}+(\vec{a} \cdot \hat{j}) \hat{j}+(\vec{a} \cdot \hat{k}) \hat{k}=x \hat{i}+y \hat{j}+z \hat{k} \\ & \end{aligned}

(\vec{a}\cdot \hat{i}) \hat{i}+(\vec{a} \cdot \hat{j}) \hat{j}+(\vec{a} \cdot \hat{k}) \hat{k}=\vec{a} \quad[\text { use }(\mathrm{i})]

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