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  • Provide solution for RD Sharma Maths Class 12 Chapter 24 Vector or Cross Product exercise Very Short Answer Question, question 20.

Provide solution for RD Sharma Maths Class 12 Chapter 24 Vector or Cross Product exercise Very Short Answer Question, question 20.

Answers (1)

ANSWER:

\frac{\pi}{4}

HINT:

Use formula of  cross product and dot product and equating them.

GIVEN:

\overrightarrow{a} and \overrightarrow{b} be two  unit vectors

SOLUTION:

Such that |\vec{a} \cdot \vec{b}|=|\vec{a} \times \vec{b}|

Let,

\theta be the angle between two vectors.

\begin{aligned} |\vec{a} \times \vec{b}| &=|\vec{a}||\vec{b}| \sin \theta \cdots(i) \\ \vec{a} \cdot \vec{b} &=\vec{a}|| \vec{b} \mid \cos \theta \cdots(i i) \end{aligned}

Equating (i) and (ii)

\begin{gathered} |\vec{a}||\vec{b}| \sin \theta=|\vec{a}||\vec{b}| \cos \theta \\ \therefore \sin \theta=1 \end{gathered}

\therefore \frac{\sin \theta}{\cos \theta }=1

\tan \theta =1

\theta =\frac{\pi}{4}

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