If |vec{c}|^2 = 60 and vec{c} times (hat{i} + | vedclass

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

Question

(D) Let $\vec{c} = a\hat{i} + b\hat{j} + c\hat{k}$.Given $\vec{c} 	imes (\hat{i} + 2\hat{j} + 5\hat{k}) = \vec{0}$,this implies that $\vec{c}$ is par

Vedclass · Accepted Answer

$12\sqrt{2}$

Vedclass · Answer

(D) Let $\vec{c} = a\hat{i} + b\hat{j} + c\hat{k}$.Given $\vec{c} 	imes (\hat{i} + 2\hat{j} + 5\hat{k}) = \vec{0}$,this implies that $\vec{c}$ is parallel to the vector $\vec{v} = \hat{i} + 2\hat{j} + 5\hat{k}$.Thus,$\vec{c} = k(\hat{i} + 2\hat{j} + 5\hat{k})$ for some scalar $k$.Given $|\vec{c}|^2 = 60$,we have $k^2(1^2 + 2^2 + 5^2) = 60$.$k^2(1 + 4 + 25) = 60 \Rightarrow 30k^2 = 60 \Rightarrow k^2 = 2 \Rightarrow k = \pm\sqrt{2}$.Taking $k = \sqrt{2}$,we get $\vec{c} = \sqrt{2}\hat{i} + 2\sqrt{2}\hat{j} + 5\sqrt{2}\hat{k}$.Now,calculate the dot product $\vec{c} \cdot (-7\hat{i} + 2\hat{j} + 3\hat{k})$:$= (\sqrt{2}\hat{i} + 2\sqrt{2}\hat{j} + 5\sqrt{2}\hat{k}) \cdot (-7\hat{i} + 2\hat{j} + 3\hat{k})$$= \sqrt{2}(-7) + 2\sqrt{2}(2) + 5\sqrt{2}(3)$$= -7\sqrt{2} + 4\sqrt{2} + 15\sqrt{2} = 12\sqrt{2}$.

If $|\vec{c}|^2 = 60$ and $\vec{c} \times (\hat{i} + 2\hat{j} + 5\hat{k}) = \vec{0}$,then a value of $\vec{c} \cdot (-7\hat{i} + 2\hat{j} + 3\hat{k})$ is

Similar Questions

Let $a = \hat{i} + x \hat{j} + \hat{k}$,$b = \hat{i} + \hat{j} + \hat{k}$ and $|a + b| = |a| + |b|$,then

If $\bar{a}$ and $\bar{b}$ are two non-parallel unit vectors and the vector $\alpha \bar{a} + \bar{b}$ bisects the internal angle between $\bar{a}$ and $\bar{b}$,then $\alpha$ is equal to

The position vectors of four points $P, Q, R, S$ are $2a + 4c$,$5a + 3\sqrt{3}b + 4c$,$-2\sqrt{3}b + c$,and $2a + c$ respectively. Then:

Show that the vector $\hat{i}+\hat{j}+\hat{k}$ is equally inclined to the axes $OX, OY,$ and $OZ$.

$a, b, c$ are non-coplanar vectors. If $a+3 b+4 c=x(a-2 b+3 c)+y(a+5 b-2 c)+z(6 a+14 b+4 c)$,then $x+y+z=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module