A and B are two vectors and θ is the angle between them, if | A × B |= 3 ( A · B ) , the value of θ is.

Correct answer: D. 60^ Finding the angle between the vectors: aligned & |A × B|= 3 (AB) & |A||B| (θ)= 3 |~A||B| (θ) aligned ) Cancelling both sides we get aligned & (θ)= 3 (θ) & ( (θ))/( (θ))= 3 & (θ)= 3 aligned ) Hence (θ=60^ ) Hence the angle between A and B is (60^ )

NEET 2007

Exam: NEET
Year: 2007
Subject: Physics
Chapter: Mathematics in Physics

NEET 2007 · Physics · Mathematics in Physics

A and B are two vectors and θ is the angle between them, if | A × B...

\vec{A}

and

\overline{\mathrm{B}}

are two vectors and

\theta

is the angle between them, if

|\overrightarrow{\mathrm{A}} \times \overline{\mathrm{B}}|=

\sqrt{3}(\overrightarrow{\mathrm{A}} \cdot \overline{\mathrm{B}})

, the value of

\theta

is.

Options

A $45^{\circ}$
B $30^{\circ}$
C $90^{\circ}$
D $60^{\circ}$

Correct answer

D. $60^{\circ}$

Step-by-step solution

Finding the angle between the vectors:

\begin{aligned} & |\mathrm{A} \times \mathrm{B}|=\sqrt{3}(\mathrm{AB}) \\ & |\mathrm{A}||\mathrm{B}| \sin (\theta)=\sqrt{3}|\mathrm{~A}||\mathrm{B}| \cos (\theta) \end{aligned}

) Cancelling both sides we get

\begin{aligned} & \sin(\theta)=\sqrt{3} \cos(\theta) \\ & \frac{\sin(\theta)}{\cos(\theta)}=\sqrt{3} \\ & \tan(\theta)=\sqrt{3} \end{aligned}

) Hence (\theta=60^{\circ}) Hence the angle between A and B is (60^{\circ})

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