If overrightarrow{ P } times overrightarrow{ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The cross product of two vectors is anti-commutative,meaning $\overrightarrow{ P } 	imes \overrightarrow{ Q } = -(\overrightarrow{ Q } 	imes \ov

Vedclass · Accepted Answer

$180$

Vedclass · Answer

(C) The cross product of two vectors is anti-commutative,meaning $\overrightarrow{ P } 	imes \overrightarrow{ Q } = -(\overrightarrow{ Q } 	imes \overrightarrow{ P })$.Given the condition $\overrightarrow{ P } 	imes \overrightarrow{ Q } = \overrightarrow{ Q } 	imes \overrightarrow{ P }$,we can substitute the anti-commutative property:$-(\overrightarrow{ Q } 	imes \overrightarrow{ P }) = \overrightarrow{ Q } 	imes \overrightarrow{ P }$.This implies $2(\overrightarrow{ Q } 	imes \overrightarrow{ P }) = 0$,so $\overrightarrow{ Q } 	imes \overrightarrow{ P } = 0$.The magnitude of the cross product is given by $|\overrightarrow{ Q } 	imes \overrightarrow{ P }| = PQ \sin 	heta = 0$.Since $P$ and $Q$ are non-zero vectors,$\sin 	heta = 0$.In the range $0^{\circ} Therefore,the value of $	heta$ is $180^{\circ}$.

If $\overrightarrow{ P } \times \overrightarrow{ Q } = \overrightarrow{ Q } \times \overrightarrow{ P }$,the angle between $\overrightarrow{ P }$ and $\overrightarrow{ Q }$ is $\theta$ $(0^{\circ} < \theta < 360^{\circ})$. The value of $\theta$ will be ........ (in $^{\circ}$)

Similar Questions

Two unit vectors $\hat{a}_{1}$ and $\hat{a}_{2}$ are inclined to each other at an angle $\theta$. If $|\hat{a}_{1}-\hat{a}_{2}|=\sqrt{3}$,then the value of $(\hat{a}_{1}-\hat{a}_{2}) \cdot (2\hat{a}_{1}-\hat{a}_{2})$ is:

If $\vec A$ and $\vec B$ are perpendicular vectors,where $\vec A = 5\hat i + 7\hat j - 3\hat k$ and $\vec B = 2\hat i + 2\hat j - a\hat k$,then the value of $a$ is:

Let $\vec{A} = 2 \hat{i} - 3 \hat{j} + 4 \hat{k}$ and $\vec{B} = 4 \hat{i} + \hat{j} + 2 \hat{k}$,then $|\vec{A} \times \vec{B}|$ is equal to:

Find the angle between the vectors $A=2 \hat{i}+4 \hat{j}+4 \hat{k}$ and $B=4 \hat{i}+2 \hat{j}-4 \hat{k}$. (in $^{\circ}$)

The dot product of unit vectors $\hat{n}_1$ and $\hat{n}_2$ that are parallel to $5 \hat{i}+12 \hat{j}$ and $3 \hat{i}+4 \hat{j}$ respectively is

Vedclass Test Series

Exam Paper Generator

Online Exam Module