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

Answers (1)

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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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