Let overline{a}, overline{b}, overline{c} be | vedclass

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

Question

(D) Given $\overline{b} \cdot \overline{c} = 10$. Since $\overline{b} \cdot \overline{c} = |\overline{b}| |\overline{c}| \cos(\frac{\pi}{3}) = 10$,we

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(D) Given $\overline{b} \cdot \overline{c} = 10$. Since $\overline{b} \cdot \overline{c} = |\overline{b}| |\overline{c}| \cos(\frac{\pi}{3}) = 10$,we have $(5) |\overline{c}| (\frac{1}{2}) = 10$,which implies $|\overline{c}| = 4$. We are given that $\overline{a}$ is perpendicular to $\overline{b} 	imes \overline{c}$,so the angle between $\overline{a}$ and $\overline{b} 	imes \overline{c}$ is $\frac{\pi}{2}$. Therefore,$|\overline{a} 	imes (\overline{b} 	imes \overline{c})| = |\overline{a}| |\overline{b} 	imes \overline{c}| \sin(\frac{\pi}{2}) = |\overline{a}| |\overline{b} 	imes \overline{c}|$. Now,$|\overline{b} 	imes \overline{c}| = |\overline{b}| |\overline{c}| \sin(\frac{\pi}{3}) = (5)(4)(\frac{\sqrt{3}}{2}) = 10\sqrt{3}$. Thus,$|\overline{a} 	imes (\overline{b} 	imes \overline{c})| = (\sqrt{3})(10\sqrt{3}) = 10 	imes 3 = 30$.

Similar Questions

If $|\vec{a}|=3$,then the value of $|\vec{a} \times \hat{i}|^2+|\vec{a} \times \hat{j}|^2+|\vec{a} \times \hat{k}|^2$ is . . . . . . .

Let the vectors $a, b, c$ and $d$ be such that $(a \times b) \times (c \times d) = 0$. Let $P_1$ and $P_2$ be planes determined by the pairs of vectors $(a, b)$ and $(c, d)$ respectively. Then the angle between $P_1$ and $P_2$ is:

$A$ unit vector perpendicular to both the vectors $\hat{i}+\hat{j}$ and $\hat{j}+\hat{k}$ is

If the area of the triangle with vertices $(1, 2, 0)$,$(1, 0, 2)$ and $(0, x, 1)$ is $\sqrt{6}$ square units,then the value of $x$ is

$A$ non-zero vector $\vec{a}$ is parallel to the line of intersection of the plane defined by $\hat{i}$ and $\hat{i} + \hat{j}$,and the plane defined by $\hat{i} - \hat{j}$ and $\hat{i} + \hat{k}$. Find the angle between $\vec{a}$ and $\hat{i} - 2\hat{j} + 2\hat{k}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module