The vector in the direction of vector 5 hat{i | vedclass

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

Question

(A) Let the given vector be $\vec{a} = 5 \hat{i} - \hat{j} + 2 \hat{k}$.First,find the magnitude of vector $\vec{a}$:$|\vec{a}| = \sqrt{5^2 + (-1)^2 +

Vedclass · Accepted Answer

$\frac{40}{\sqrt{30}} \hat{i} - \frac{8}{\sqrt{30}} \hat{j} + \frac{16}{\sqrt{30}} \hat{k}$

Vedclass · Answer

(A) Let the given vector be $\vec{a} = 5 \hat{i} - \hat{j} + 2 \hat{k}$.First,find the magnitude of vector $\vec{a}$:$|\vec{a}| = \sqrt{5^2 + (-1)^2 + 2^2} = \sqrt{25 + 1 + 4} = \sqrt{30}$.The unit vector in the direction of $\vec{a}$ is given by $\hat{a} = \frac{\vec{a}}{|\vec{a}|} = \frac{5 \hat{i} - \hat{j} + 2 \hat{k}}{\sqrt{30}}$.$A$ vector of magnitude $8$ units in the direction of $\vec{a}$ is $8 \hat{a} = 8 	imes \left( \frac{5 \hat{i} - \hat{j} + 2 \hat{k}}{\sqrt{30}} ight) = \frac{40}{\sqrt{30}} \hat{i} - \frac{8}{\sqrt{30}} \hat{j} + \frac{16}{\sqrt{30}} \hat{k}$.Thus,the correct option is $A$.

The vector in the direction of vector $5 \hat{i} - \hat{j} + 2 \hat{k}$ with a magnitude of $8$ units is:

Similar Questions

In a regular hexagon $ABCDEF$,$AD + EB + FC = (3\lambda - 8) AB$. Then $\lambda =$

The direction cosines of the resultant of the vectors $(i + j + k)$,$(-i + j + k)$,$(i - j + k)$ and $(i + j - k)$ are

$3\overrightarrow{OD} + \overrightarrow{DA} + \overrightarrow{DB} + \overrightarrow{DC} = $

$A$ unit vector in $XY$-plane making an angle $45^{\circ}$ with $\hat{i}+\hat{j}$ and an angle $60^{\circ}$ with $3\hat{i}-4\hat{j}$ is

If $ABCD$ is a parallelogram with $AC$ and $BD$ as diagonals,then which of the following is true regarding the vector relationship between the diagonals and sides?

Vedclass Test Series

Exam Paper Generator

Online Exam Module