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  • Explain solution RD Sharma class 12 chapter Vector or Cross Product exercise 24.1 question 32 maths

Explain solution RD Sharma class 12 chapter Vector or Cross Product exercise 24.1 question 32 maths

Answers (1)

Answer:

 No, take any two collinear vectors

Hint:

To solve this we let

\hat{i}+\hat{j}+\hat{k}=\overrightarrow{0} ; 2 \hat{i}+2 \hat{j}+2 \hat{k}=\overrightarrow{0}

Given: \vec{a}=0 ; \vec{b}=0 \text { then } \vec{a} \times \vec{b}=0

Solution:

Statement:

If either \vec{a}=\vec{b} \text { or } \vec{b}=\overrightarrow{0} \Rightarrow \vec{a} \times \vec{b}=0

Converse: \vec{a}=0 ; \vec{b}=0 \text { then } \vec{a} \times \vec{b}=0

Let 

\begin{aligned} &\vec{a}=\hat{i}+\hat{j}+\hat{k}=(1,1,1) \\\\ &\vec{b}=2 \hat{i}+2 \hat{j}+2 \hat{k}=(2,2,2) \end{aligned}

\begin{aligned} &\vec{a} \times \vec{b}=\left|\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & 1 \\ 2 & 2 & 2 \end{array}\right| \\\\ &=\hat{i}(2-2)+\hat{j}(2-2)+\hat{k}(2-2) \\\\ &=\vec{o} \end{aligned}

But  \vec{a} \neq 0 \text { and } \vec{b} \neq 0

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