Given two vectors vec{A} = 3hat{i} + hat{j} a | vedclass

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

Question

(C) The area of a parallelogram formed by two adjacent vectors $\vec{A}$ and $\vec{B}$ is given by the magnitude of their cross product: $	ext{Area}

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(C) The area of a parallelogram formed by two adjacent vectors $\vec{A}$ and $\vec{B}$ is given by the magnitude of their cross product: $	ext{Area} = |\vec{A} 	imes \vec{B}|$.First,calculate the cross product $\vec{A} 	imes \vec{B}$:$\vec{A} 	imes \vec{B} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 3 & 1 & 0 \ 0 & 1 & 2 \end{vmatrix}$$= \hat{i}(1 	imes 2 - 0 	imes 1) - \hat{j}(3 	imes 2 - 0 	imes 0) + \hat{k}(3 	imes 1 - 1 	imes 0)$$= \hat{i}(2) - \hat{j}(6) + \hat{k}(3) = 2\hat{i} - 6\hat{j} + 3\hat{k}$.Now,calculate the magnitude of this vector:$|\vec{A} 	imes \vec{B}| = \sqrt{(2)^2 + (-6)^2 + (3)^2}$$= \sqrt{4 + 36 + 9} = \sqrt{49} = 7$.Thus,the area of the parallelogram is $7$ square units.

Given two vectors $\vec{A} = 3\hat{i} + \hat{j}$ and $\vec{B} = \hat{j} + 2\hat{k}$. If these two vectors represent the adjacent sides of a parallelogram,find the area of the parallelogram.

Similar Questions

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

What is the unit vector perpendicular to the vectors $2\hat i + 2\hat j - \hat k$ and $6\hat i - 3\hat j + 2\hat k$?

$A$ vector perpendicular to $\hat{i}+\hat{j}+\hat{k}$ is:

$\vec{A}$ is a vector quantity such that $|\vec{A}| =$ nonzero constant. Which of the following expressions is true for $\vec{A}$?

For two vectors $\vec{P}$ and $\vec{Q}$, $\vec{P} \cdot \vec{Q} = |\vec{P} \times \vec{Q}|$. The magnitude of $\vec{R} = \vec{P} + \vec{Q}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module