If |vec{a} times vec{b}|^{2}+|vec{a} cdot vec | vedclass

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

Question

(C) Given that,$|\vec{a} 	imes \vec{b}|^{2}+|\vec{a} \cdot \vec{b}|^{2}=144$ and $|\vec{a}|=4$. We know the Lagrange's identity for vectors: $|\vec{a

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) Given that,$|\vec{a} 	imes \vec{b}|^{2}+|\vec{a} \cdot \vec{b}|^{2}=144$ and $|\vec{a}|=4$. We know the Lagrange's identity for vectors: $|\vec{a} 	imes \vec{b}|^{2}+|\vec{a} \cdot \vec{b}|^{2}=|\vec{a}|^{2} |\vec{b}|^{2} \sin^{2} 	heta + |\vec{a}|^{2} |\vec{b}|^{2} \cos^{2} 	heta$. Factoring out $|\vec{a}|^{2} |\vec{b}|^{2}$,we get: $|\vec{a}|^{2} |\vec{b}|^{2} (\sin^{2} 	heta + \cos^{2} 	heta) = |\vec{a}|^{2} |\vec{b}|^{2}$. Therefore,$|\vec{a} 	imes \vec{b}|^{2}+|\vec{a} \cdot \vec{b}|^{2}=|\vec{a}|^{2} |\vec{b}|^{2}$. Substituting the given values: $144 = (4)^{2} |\vec{b}|^{2}$. $144 = 16 |\vec{b}|^{2}$. $|\vec{b}|^{2} = \frac{144}{16} = 9$. Taking the square root,we get $|\vec{b}| = 3$.

If $|\vec{a} \times \vec{b}|^{2}+|\vec{a} \cdot \vec{b}|^{2}=144$ and $|\vec{a}|=4$,then the value of $|\vec{b}|$ is

Similar Questions

$A$ force of magnitude $6$ acts along the vector $(9, 6, -2)$ and passes through a point $A(4, -1, -7)$. The moment of the force about the point $O(1, -3, 2)$ is

If $U = [2, -3, 4]$,$X = [0, 2, 3]$,$V = \begin{bmatrix} 3 \\ 2 \\ 1 \end{bmatrix}$ and $Y = \begin{bmatrix} 2 \\ 2 \\ 4 \end{bmatrix}$,then $UV + XY = $?

The unit vector in $ZOX$ plane, making angles $45^{\circ}$ and $60^{\circ}$ respectively with $\vec{\alpha}=2 \hat{i}+2 \hat{j}-\hat{k}$ and $\vec{\beta}=\hat{j}-\hat{k}$ is

Find the angle between the pair of lines given by $\vec{r}=3 \hat{i}+2 \hat{j}-4 \hat{k}+\lambda(\hat{i}+2 \hat{j}+2 \hat{k})$ and $\vec{r}=5 \hat{i}-2 \hat{j}+\mu(3 \hat{i}+2 \hat{j}+6 \hat{k})$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module