Download App

VECTOR ALGEBRA — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVECTOR ALGEBRA2 Marks
Question
Find the angle between the vectora $\vec{\text{a}}=\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}}.$
✓

Answer

We have
$\vec{\text{a}}=\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}}$
Let $\theta$ be the angle between $\vec{\text{a}}$ and $\vec{\text{b}}.$
$|\vec{\text{a}}|=\sqrt{(1)^2+(-1)^2+(1)^2}=\sqrt{3}$
$\big|\vec{\text{b}}\big|=\sqrt{(1)^2+(1)^2+(-1)^2}=\sqrt{3}$
and
$\vec{\text{a}}.\vec{\text{b}}=1-1-1=-1$
Now,
$\cos\theta=\frac{\vec{\text{a}}.\vec{\text{b}}}{|\vec{\text{a}}|\big|\vec{\text{b}}\big|}=\frac{-1}{\sqrt{3}\sqrt{3}}=\frac{-1}{3}$
$\therefore\theta=\cos^-1\big(\frac{-1}{3}\big)$

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 VECTOR ALGEBRA→VECTOR ALGEBRA — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are unit vectors, then write the value of $\big|\vec{\text{a}}\times\vec{\text{b}}\big|^2+\big(\vec{\text{a}}.\vec{\text{b}}\big)^2.$
→
If two vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ are such that $|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=1$ and $\vec{\text{a}}.\vec{\text{b}}=1,$ then find the value of $\big(3\vec{\text{a}}-5\vec{\text{b}}\big).\big(2\vec{\text{a}}+7\vec{\text{b}}\big).$
→
If x and y are connected parametrically by the equations given in Exercise without eliminating the parameter, Find $\frac{\text{dy}}{\text{dx}}.$
$\text{x}=4\text{t, y}=\frac{4}{\text{t}}$
→
If $\text{A}=\begin{bmatrix}1&1\\1&1\end{bmatrix}$ satisfies $\text{A}^4=\lambda\text{A},$ then write the value of $\lambda.$
→
If $R$ is a symmetric relation on a set $A,$ then write a relation between $R$ and $R^{-1}.$
→
Simplify $\cos \theta \left[ \begin{array} { c c } { \cos \theta } & { \sin \theta } \\ { - \sin \theta } & { \cos \theta } \end{array} \right] + \sin \theta \left[ \begin{array} { c c } { \sin \theta } & { - \cos \theta } \\ { \cos \theta } & { \sin \theta } \end{array} \right]$.
→
Determine the direction cosines of the normal to the plane and the distance from the origin.
5y + 8 = 0
→
Evaluate the following integrals:
$\int\Big(\frac{\text{m}}{\text{x}}+\frac{\text{x}}{\text{m}}+\text{m}^\text{x}+\text{x}^\text{m}+\text{mx}\Big)\text{dx}$
→
Evaluate the following definite integrals:
$\int_{0}^\limits{1}\frac{1}{1+\text{x}^2} \text{ dx}$
→
Determine whether $f(x)=-\frac{\pi}{2}+$ sin x is increasing or decreasing on $\left(-\frac{\pi}{3}, \frac{\pi}{3}\right)$
→