Given |vec{A}_1|=2, |vec{A}_2|=3 and |vec{A}_ | vedclass

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

Question

(A) Given that $|\vec{A}_1|=2, |\vec{A}_2|=3$ and $|\vec{A}_1+\vec{A}_2|=3$. Squaring the magnitude of the sum: $(|\vec{A}_1+\vec{A}_2|)^2 = 3^2$ $A_1

Vedclass · Accepted Answer

$-64$

Vedclass · Answer

(A) Given that $|\vec{A}_1|=2, |\vec{A}_2|=3$ and $|\vec{A}_1+\vec{A}_2|=3$. Squaring the magnitude of the sum: $(|\vec{A}_1+\vec{A}_2|)^2 = 3^2$ $A_1^2 + A_2^2 + 2 \vec{A}_1 \cdot \vec{A}_2 = 9$ $4 + 9 + 2 \vec{A}_1 \cdot \vec{A}_2 = 9$ $13 + 2 \vec{A}_1 \cdot \vec{A}_2 = 9$ $2 \vec{A}_1 \cdot \vec{A}_2 = -4$ $\vec{A}_1 \cdot \vec{A}_2 = -2$ Now,expand the expression $(\vec{A}_1+2 \vec{A}_2) \cdot (3 \vec{A}_1-4 \vec{A}_2)$: $= 3 \vec{A}_1 \cdot \vec{A}_1 - 4 \vec{A}_1 \cdot \vec{A}_2 + 6 \vec{A}_2 \cdot \vec{A}_1 - 8 \vec{A}_2 \cdot \vec{A}_2$ $= 3 |\vec{A}_1|^2 + 2 \vec{A}_1 \cdot \vec{A}_2 - 8 |\vec{A}_2|^2$ Substitute the values: $= 3(2)^2 + 2(-2) - 8(3)^2$ $= 3(4) - 4 - 8(9)$ $= 12 - 4 - 72$ $= 8 - 72 = -64$

Given $|\vec{A}_1|=2, |\vec{A}_2|=3$ and $|\vec{A}_1+\vec{A}_2|=3$. Find the value of $(\vec{A}_1+2 \vec{A}_2) \cdot (3 \vec{A}_1-4 \vec{A}_2)$ :

Similar Questions

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

If $\vec A$ and $\vec B$ are perpendicular vectors,where $\vec A = 5\hat i + 7\hat j - 3\hat k$ and $\vec B = 2\hat i + 2\hat j - a\hat k$,then the value of $a$ is:

$A$ force $F$ applied on a body is written as $F = (\hat{n} \cdot F) \hat{n} + G$,where $\hat{n}$ is a unit vector. The vector $G$ is equal to

The angle between force $\vec{F}=3 \hat{i}+4 \hat{j}-5 \hat{k}$ and displacement $\vec{d}=5 \hat{i}+4 \hat{j}+3 \hat{k}$ is

The value of $(\overrightarrow A + \overrightarrow B ) \times (\overrightarrow A - \overrightarrow B )$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module