Find a unit vector in the direction of the vector a =3 i -2 j +6 … - Vidyadip

Question

Find a unit vector in the direction of the vector $\vec{\text{a}}=3\hat{\text{i}}-2\hat{\text{j}}+6\hat{\text{k}}$.

✓

Answer

Given: $\vec{\text{a}}=3\hat{\text{i}}-2\hat{\text{j}}+6\hat{\text{k}}$ Then, $|\vec{\text{a}}|=\sqrt{3^2+(-2)^2+6^2}$ $=\sqrt{9+4+36}$ $=\sqrt{49}$ $=7$ $\therefore$ Unit vector $=\frac{\vec{\text{a}}}{|\vec{\text{a}}|}=\frac{3\hat{\text{i}}-2\hat{\text{j}}+6\hat{\text{k}}}7$$=\frac{3}7\hat{\text{i}}-\frac{2}7\hat{\text{j}}+\frac{6}7\hat{\text{k}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Algebra of Vectors→Algebra of Vectors — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\text{y}=\mid\log_\text{e}\text{x}\mid $ find $\frac{\text{d}^2\text{y}}{\text{dx}^2}$

Verify that the function $y=e^{x}(a \cos x+b \sin x)\ ($implicit or explicit$)$ is a solution of the differential equation $\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+2 y=0$

Write the point where $\text{f}(\text{x})=\text{x}\log_{\text{e}}\text{x}$ attains minimum value.

Find the angle between the vectora $\vec{\text{a}}=\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}}.$

Find x, y satisfying the matrix equation.
$\begin{bmatrix}\text{x}-\text{y}&2&-2\\4&\text{x}&6\end{bmatrix}+\begin{bmatrix}3&-2&2\\1&0&-1\end{bmatrix}=\begin{bmatrix}6&0&0\\5&2\text{x}+\text{y}&5\end{bmatrix}$

Find the Cartesian equation of the following plane:$\vec{\text{r}}.\Big(2\hat{\text{i}}+3\hat{\text{j}}-4\hat{\text{k}}\Big)=1$

A discrete random variable $X$ has the probability distribution given below:

$X:$	$0.5$	$1$	$1.5$	$2$
$P(X):$	$k$	$k^2$	$2k^2$	$k$

Determine the mean of the distribution.

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two vectors of magnitudes 3 and $\frac{\sqrt{2}}{3}$ repectively such that $\vec{\text{a}}\times\vec{\text{b}}$ is a unit vector. write the angle between $\vec{\text{a}}$ and $\vec{\text{b}}.$

If $|\vec{a}|=10,|\vec{b}|=2, \vec{a} \cdot \vec{b}=12$, then find the value of $\vec{a} \times \vec{b}$.

If $x$ and $y$ are connected parametrically by the equations given in Exercise without eliminating the parameter, Find $\frac{\text{dy}}{\text{dx}}.\text{x}=\text{a}\cos\theta,\text{y}=\text{b}\cos\theta$