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  • Please solve RD Sharma class 12 chapter 23 Scaler and Dot Product exercise Multiple choice question 17 maths textbook solution

Please solve RD Sharma class 12 chapter 23 Scaler and Dot Product exercise Multiple choice question 17 maths textbook solution

Answers (1)

Answer:

Option (b) a=4, b=4, c=5

Hint:

Use the formula of \vec{a} \text { and } \vec{b} , when \vec{a} \text { and } \vec{b} are perpendicular \vec{a} \cdot \vec{b}=0

Given:

2 \hat{i}+3 \hat{j}-4 \hat{k} \text { and } \hat{a} \hat{i}+b \hat{j}+c \hat{k}  are perpendicular

Solution:

Given that,

2 \hat{i}+3 \hat{j}-4 \hat{k} \text { and } \hat{a} \hat{i}+b \hat{j}+c \hat{k}  are perpendicular

\begin{aligned} \therefore &(2 \hat{i}+3 \hat{j}-4 \hat{k}) \cdot(\hat{a} \hat{i}+b \hat{j}+c \hat{k})=0 \\\\ & 2 a+3 b-4 c=0 \end{aligned}

For option (a),

\begin{aligned} &a=2, b=3, c=-4 \\\\ &2(2)+3(3)-4(-4) \\\\ &=4+9+16=29 \\\\ &29 \neq 0 \end{aligned}

Hence, option (a) is not correct

For option (b),

\begin{aligned} &a=4, b=4, c=5 \\\\ &2(4)+3(4)-4(5) \\\\ &=8+12-20 \\\\ &0=0 \end{aligned}

Hence, option (b) is correct

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