If |A|=2, |B|=5 and |A times B|=8. If the ang | vedclass

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

Question

(A) Given: $|A|=2, |B|=5$ and $|A 	imes B|=8$.We know that the magnitude of the cross product is given by $|A 	imes B| = |A| |B| \sin 	heta$.Substi

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(A) Given: $|A|=2, |B|=5$ and $|A 	imes B|=8$.We know that the magnitude of the cross product is given by $|A 	imes B| = |A| |B| \sin 	heta$.Substituting the values: $8 = (2)(5) \sin 	heta$.$8 = 10 \sin 	heta \implies \sin 	heta = 8/10 = 4/5$.Since the angle $	heta$ is acute,$\cos 	heta$ must be positive.Using the identity $\cos 	heta = \sqrt{1 - \sin^2 	heta} = \sqrt{1 - (4/5)^2} = \sqrt{1 - 16/25} = \sqrt{9/25} = 3/5$.The dot product is given by $A \cdot B = |A| |B| \cos 	heta$.Substituting the values: $A \cdot B = (2)(5)(3/5) = 10 	imes (3/5) = 6$.

If $|A|=2, |B|=5$ and $|A \times B|=8$. If the angle between $A$ and $B$ is acute,then $A \cdot B$ is

Similar Questions

The area of the triangle formed by the vectors $\vec{a} = 2\hat{i} + \hat{j} - \hat{k}$ and $\vec{b} = \hat{i} + \hat{j} + \hat{k}$ is:

The angle between the vectors $(\hat{i} + \hat{j})$ and $(\hat{i} - \hat{k})$ is ........ $^\circ$.

If $\overrightarrow{A} = (2\hat{i} + 3\hat{j} - \hat{k}) \; m$ and $\overrightarrow{B} = (\hat{i} + 2\hat{j} + 2\hat{k}) \; m$,the magnitude of the component of vector $\overrightarrow{A}$ along vector $\overrightarrow{B}$ will be $...... \; m$.

Find the angle between two vectors $\vec A = 2\hat i + \hat j - \hat k$ and $\vec B = \hat i - \hat k$ in degrees.

$\vec{A}$,$\vec{B}$,and $\vec{C}$ are three non-collinear,non-coplanar vectors. What can you say about the direction of $\vec{A} \times (\vec{B} \times \vec{C})$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module