If the vectors 2 hat{i}-3 hat{j}+6 hat{k} and | vedclass

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

Question

(C) Let $\vec{a} = 2 \hat{i}-3 \hat{j}+6 \hat{k}$.Since $\vec{b}$ is collinear to $\vec{a}$,we can write $\vec{b} = \lambda \vec{a}$ for some scalar $

Vedclass · Accepted Answer

$4 \hat{i}-6 \hat{j}+12 \hat{k}$

Vedclass · Answer

(C) Let $\vec{a} = 2 \hat{i}-3 \hat{j}+6 \hat{k}$.Since $\vec{b}$ is collinear to $\vec{a}$,we can write $\vec{b} = \lambda \vec{a}$ for some scalar $\lambda$.The magnitude of $\vec{a}$ is $|\vec{a}| = \sqrt{2^2 + (-3)^2 + 6^2} = \sqrt{4 + 9 + 36} = \sqrt{49} = 7$.The unit vector in the direction of $\vec{a}$ is $\hat{a} = \frac{\vec{a}}{|\vec{a}|} = \frac{2 \hat{i}-3 \hat{j}+6 \hat{k}}{7}$.Given $|\vec{b}| = 14$,the vector $\vec{b}$ can be expressed as $\vec{b} = \pm |\vec{b}| \hat{a}$.Taking the positive direction,$\vec{b} = 14 \left( \frac{2 \hat{i}-3 \hat{j}+6 \hat{k}}{7} \right) = 2(2 \hat{i}-3 \hat{j}+6 \hat{k}) = 4 \hat{i}-6 \hat{j}+12 \hat{k}$.

If the vectors $2 \hat{i}-3 \hat{j}+6 \hat{k}$ and $\vec{b}$ are collinear and $|\vec{b}|=14$,then $\vec{b}$ has the value

Similar Questions

If the points with position vectors $10\hat{i} + 3\hat{j}$,$12\hat{i} - 5\hat{j}$,and $a\hat{i} + 11\hat{j}$ are collinear,then the value of $a$ is:

The projection of the vector $i+j+k$ along the vector $j$ is

Find the unit vector in the direction of the vector $\vec{a} = \hat{i} + \hat{j} + 2\hat{k}$.

If $a = \hat{i} + 2 \hat{j} + 3 \hat{k}$,$b = 2 \hat{i} + 3 \hat{j} + \hat{k}$,$c = 8 \hat{i} + 13 \hat{j} + 9 \hat{k}$ and $x a + y b + z c = 0$,then $\frac{x y}{z^2} =$

The position vectors of $P$ and $Q$ are respectively $\overrightarrow{a}$ and $\overrightarrow{b}$. If $R$ is a point on the line $PQ$ such that $\overrightarrow{PR}=5 \overrightarrow{PQ}$,then the position vector of $R$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module