If overrightarrow{A} times overrightarrow{B} | vedclass

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

Question

(D) By the definition of the cross product,the vector $\overrightarrow{C} + \overrightarrow{D}$ is perpendicular to both $\overrightarrow{A}$ and $\ov

Vedclass · Accepted Answer

Component of $\overrightarrow{C}$ along $\overrightarrow{A} = -$ component of $\overrightarrow{D}$ along $\overrightarrow{A}$

Vedclass · Answer

(D) By the definition of the cross product,the vector $\overrightarrow{C} + \overrightarrow{D}$ is perpendicular to both $\overrightarrow{A}$ and $\overrightarrow{B}$.Therefore,the dot product of $\overrightarrow{A}$ with $(\overrightarrow{C} + \overrightarrow{D})$ must be zero:$\overrightarrow{A} \cdot (\overrightarrow{C} + \overrightarrow{D}) = 0$Expanding this,we get:$\overrightarrow{A} \cdot \overrightarrow{C} + \overrightarrow{A} \cdot \overrightarrow{D} = 0$Since the component of a vector $\vec{V}$ along $\vec{A}$ is given by $\frac{\vec{V} \cdot \vec{A}}{|A|}$,we can write:$|A| 	imes (	ext{component of } \overrightarrow{C} 	ext{ along } \overrightarrow{A}) + |A| 	imes (	ext{component of } \overrightarrow{D} 	ext{ along } \overrightarrow{A}) = 0$Dividing by $|A|$ (assuming $\overrightarrow{A} 
eq 0$):Component of $\overrightarrow{C}$ along $\overrightarrow{A} = -$ component of $\overrightarrow{D}$ along $\overrightarrow{A}$.

If $\overrightarrow{A} \times \overrightarrow{B} = \overrightarrow{C} + \overrightarrow{D},$ then select the correct alternative-

Similar Questions

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 $^{\circ}$)

If $a + b + c = 0$,then $a \times b$ is equal to:

Consider a vector $\overrightarrow{F} = 4\hat{i} - 3\hat{j}$. Another vector that is perpendicular to $\overrightarrow{F}$ is

For what value of $x$ will the two vectors $\vec{A} = 2\hat{i} + 2\hat{j} - x\hat{k}$ and $\vec{B} = 2\hat{i} - \hat{j} - 3\hat{k}$ be perpendicular to each other?

If $\vec{A} = 2\hat{i} + 3\hat{j} + 8\hat{k}$ is perpendicular to $\vec{B} = -4\hat{i} + 4\hat{j} + \alpha\hat{k}$,then the value of $\alpha$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module