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

If $\overrightarrow A = 3\hat i + \hat j + 2\hat k$ and $\overrightarrow B = 2\hat i - 2\hat j + 4\hat k$,then find $|\overrightarrow A \times \overrightarrow B |$.

Explain the geometrical interpretation of the scalar product of two vectors.

The angle between vectors $(\overrightarrow {A} \times \overrightarrow {B})$ and $(\overrightarrow {B} \times \overrightarrow {A})$ is

The vectors $\overrightarrow P = a\hat i + a\hat j + 3\hat k$ and $\overrightarrow Q = a\hat i - 2\hat j - \hat k$ are perpendicular to each other. The positive value of $a$ is

Find the angle between the two vectors: $\vec{a}=3 \hat{i}+2 \hat{j}+5 \hat{k}$ and $\vec{b}=5 \hat{i}+3 \hat{j}+\hat{k}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module