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  • Need solution for RD Sharma Maths Class 12 Chapter 23 Scalar or Dot Products Excercise Very Short Answer Question 22

Need solution for RD Sharma Maths Class 12 Chapter 23 Scalar or Dot Products Excercise Very Short Answer Question 22

Answers (1)

Answer :-  \hat{i}

Hint :- Use the general form of any vector

Given :-  \vec{a} \cdot \hat{\imath}=\vec{a}(\hat{\imath}+\hat{\jmath})=\vec{a}(\hat{l}+\hat{\jmath}+\hat{k})=1

Solution :-  \vec{a}=x \hat{i}+y \hat{\jmath}+z \hat{k}  (?general form)

\begin{aligned} &\Rightarrow(x \hat{\imath}+y \hat{\jmath}+z \hat{k}) \cdot \hat{l}=(x \hat{\imath}+y \hat{\jmath}+z \hat{k})(\hat{\imath}+\hat{\jmath})=(x \hat{\imath}+y \hat{\jmath}+z \hat{k})(\hat{\imath}+\hat{\jmath}+\hat{k})=1 \\ & \end{aligned}

\Rightarrow x+0+0=x+y+0=x+y+z=1 \\

\Rightarrow x=1, y+x=1 \& x+y+z=1

Now,

\begin{aligned} &\Rightarrow y+1=0(\because x=1) \\ & \end{aligned}

\Rightarrow y=1

and  x+y+z=1

\begin{aligned} &\Rightarrow 1+0+z=1 \quad(\because x=1 \& y=0) \\ & \end{aligned}

\Rightarrow z=0

 

Posted by

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