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  • Explain solution RD Sharma class 12 chapter 25 Scalar triple product exercise multiple choice question 12 maths

Explain solution RD Sharma class 12 chapter 25 Scalar triple product exercise multiple choice question 12 maths

Answers (1)

Answer:

 \overrightarrow{a}.\overrightarrow{b}=0,\overrightarrow{b}.\overrightarrow{c}=0,\overrightarrow{c}.\overrightarrow{a}=0

Hint:

 Use scalar triple product

Given:

(\overrightarrow{a}.\overrightarrow{b}).\overrightarrow{c}=\left | \overrightarrow{a} \right |\left | \overrightarrow{b} \right |\left | \overrightarrow{c} \right |

For

(\overrightarrow{a}.\overrightarrow{b}).\overrightarrow{c}=\left | \overrightarrow{a}\times \overrightarrow{b} \right |\left | \overrightarrow{c} \right |cos\theta

where,

\theta is angle between cross product of

(\overrightarrow{a}\times \overrightarrow{b}) \text { and }\overrightarrow{c}

Similarly,

(\overrightarrow{a}\times \overrightarrow{b}) .\overrightarrow{c}=\left ( \left | \overrightarrow{a} \right |\left | \overrightarrow{b} \right |sin\beta \right ).\overrightarrow{c}

where

\beta is angle between

\overrightarrow{a} \text { and } \overrightarrow{b}

Thus, for all

\overrightarrow{a}.\overrightarrow{b}=0,\overrightarrow{b}.\overrightarrow{c}=0,\overrightarrow{c}.\overrightarrow{a}=0

Posted by

Gurleen Kaur

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