What is the angle between the resultant of ov | vedclass

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

Question

(C) Let $\overrightarrow{A}$ and $\overrightarrow{B}$ be two vectors in a plane. The sum $\overrightarrow{A} + \overrightarrow{B}$ is a vector that li

Vedclass · Accepted Answer

$\frac{\pi}{2} 	ext{ rad}$

Vedclass · Answer

(C) Let $\overrightarrow{A}$ and $\overrightarrow{B}$ be two vectors in a plane. The sum $\overrightarrow{A} + \overrightarrow{B}$ is a vector that lies in the same plane as $\overrightarrow{A}$ and $\overrightarrow{B}$.By the definition of the cross product,$\overrightarrow{A} 	imes \overrightarrow{B}$ is a vector that is perpendicular to the plane containing both $\overrightarrow{A}$ and $\overrightarrow{B}$.Since the vector $(\overrightarrow{A} + \overrightarrow{B})$ lies in the plane and the vector $(\overrightarrow{A} 	imes \overrightarrow{B})$ is perpendicular to the plane,the angle between them is $90^{\circ}$ or $\frac{\pi}{2} 	ext{ rad}$.Mathematically,the dot product of these two vectors is:$(\overrightarrow{A} + \overrightarrow{B}) \cdot (\overrightarrow{A} 	imes \overrightarrow{B}) = \overrightarrow{A} \cdot (\overrightarrow{A} 	imes \overrightarrow{B}) + \overrightarrow{B} \cdot (\overrightarrow{A} 	imes \overrightarrow{B})$Using the property of the scalar triple product,$\overrightarrow{A} \cdot (\overrightarrow{A} 	imes \overrightarrow{B}) = 0$ and $\overrightarrow{B} \cdot (\overrightarrow{A} 	imes \overrightarrow{B}) = 0$.Therefore,$(\overrightarrow{A} + \overrightarrow{B}) \cdot (\overrightarrow{A} 	imes \overrightarrow{B}) = 0$,which confirms that the vectors are orthogonal,and the angle between them is $90^{\circ}$.

What is the angle between the resultant of $\overrightarrow{A} + \overrightarrow{B}$ and $\overrightarrow{A} \times \overrightarrow{B}$?

Similar Questions

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

Three vectors $\vec{A}, \vec{B}$ and $\vec{C}$ are such that $\vec{A} \cdot \vec{B} = 0$ and $\vec{A} \cdot \vec{C} = 0$. Then $\vec{A}$ is parallel to:

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

Show that the magnitude of a vector is equal to the square root of the scalar product of the vector with itself.

$A$ vector $\vec{A}$ points towards North and vector $\vec{B}$ points upwards,then $\vec{A} \times \vec{B}$ points towards ...........

Vedclass Test Series

Exam Paper Generator

Online Exam Module