If |vec{a}|=10, |vec{b}|=2 and vec{a} cdot ve | vedclass

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

Question

(C) We know that for any two vectors $\vec{a}$ and $\vec{b}$,the relationship between their dot product and cross product is given by the identity: $|

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(C) We know that for any two vectors $\vec{a}$ and $\vec{b}$,the relationship between their dot product and cross product is given by the identity: $|\vec{a} 	imes \vec{b}|^2 + (\vec{a} \cdot \vec{b})^2 = |\vec{a}|^2 |\vec{b}|^2$ Given values are $|\vec{a}|=10$,$|\vec{b}|=2$,and $\vec{a} \cdot \vec{b}=12$. Substituting these values into the identity: $|\vec{a} 	imes \vec{b}|^2 + (12)^2 = (10)^2 (2)^2$ $|\vec{a} 	imes \vec{b}|^2 + 144 = 100 	imes 4$ $|\vec{a} 	imes \vec{b}|^2 + 144 = 400$ $|\vec{a} 	imes \vec{b}|^2 = 400 - 144$ $|\vec{a} 	imes \vec{b}|^2 = 256$ Taking the square root on both sides: $|\vec{a} 	imes \vec{b}| = \sqrt{256} = 16$ Therefore,the correct option is $C$.

If $|\vec{a}|=10, |\vec{b}|=2$ and $\vec{a} \cdot \vec{b}=12$,then $|\vec{a} \times \vec{b}|=$ . . . . . . .

Similar Questions

$A$ vector of length $3$ perpendicular to each of the vectors $3\,i + j - 4\,k$ and $6\,i + 5\,j - 2\,k$ is

$A$ unit vector perpendicular to the plane containing the vectors $\hat{i}+2\hat{j}+\hat{k}$ and $-2\hat{i}+\hat{j}+3\hat{k}$ is

If the two diagonals of a parallelogram are $\bar{d_1} = \bar{i} + 2\bar{j} + 3\bar{k}$ and $\bar{d_2} = -2\bar{i} + \bar{j} - 2\bar{k}$,then the area of the parallelogram in square units is

If $u = a - b$ and $v = a + b$ and $|a| = |b| = 2$,then $|u \times v|$ is equal to

If $u = 2i + 2j - k$ and $v = 6i - 3j + 2k,$ then a unit vector perpendicular to both $u$ and $v$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module