Download App

VECTOR ALGEBRA — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVECTOR ALGEBRA2 Marks
Question
vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ are such that $|\vec{\text{a}}|=\sqrt{3},\big|\vec{\text{b}}\big|=\frac{2}{3}$ and $\big(\vec{\text{a}}\times\vec{\text{b}}\big)$ is a unit vector. write the angle between $\vec{\text{a}}$ and $\vec{\text{b}}.$
✓

Answer

Given: $\vec{\text{a}}\times\vec{\text{b}}$ is a unit vector.
$\Rightarrow\big|\vec{\text{a}}\times\vec{\text{b}}\big|=1\dots(1)$
Let $\theta$ be the angle between $\vec{\text{a}}$ and $\vec{\text{b}}.$
We know
$\big|\vec{\text{a}}\times\vec{\text{b}}\big|=|\vec{\text{a}}|\big|\vec{\text{b}}\big|\sin\theta$
From (1), we get
$1=(\sqrt{3})\Big(\frac{2}{3}\Big)\sin\theta$
$\Rightarrow\sin\theta=\frac{\sqrt{3}}{2}$
$\Rightarrow\theta=\frac{\pi}{3}$

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 $\text{f(x)}=\begin{cases}\frac{\text{x}^2-16}{\text{x}-4},&\text{if }\text{ x}\neq4\\\text{k},&\text{if }\text{ x}=4\end{cases}$ is continuous at x = 4, find k.
→
Write the minimum value of $\text{f}(\text{x})=\text{x}+\frac{1}{\text{x}},\text{x}>0.$
→
If $A$ and $B$ are symmetric matrices of the same order, write whether $AB − BA$ is symmetric or skew-symmetric or neither of the two.
→
Evaluate the following determinant: $\begin{vmatrix}67&19&21\\39&13&14\\81&24&26 \end{vmatrix}$
→
Evaluate the following definite integrals:
$\int_{0}^\limits{\frac{\pi}{2}}(\sin\text{x}+\cos\text{x})\text{dx}$
→
Write the direction consines of the line whose cartesian equations are 2x = 3y = -z.
→
If |x| < 1 and $\text{y}=1+\text{x}+\text{x}^2+\ .....\ \text{to}\ \infty,$ then find the value of $\frac{\text{dy}}{\text{dx}}.$
→
Write the domain of the real function f defined by $\text{f(x)}=\sqrt{25-\text{x}^2}.$
→
Find the number of all onto functions from the set A = {1, 2, 3, ..., n} to itself.
→
Find the maximum and minimum value, f(x) = |x + 2| - 1
→