Download App

Vector Algebra — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVector Algebra2 Marks
Question
Find the angle between two vectors $\vec a$ and $\vec b$ with magnitudes $\sqrt 3 $ and 2, respectively, having $\vec a\;.\vec b = \sqrt 6 $
✓

Answer

$ \left| {\overrightarrow a } \right| = \sqrt 3 ,\left| {\overrightarrow b } \right| = 2,\overrightarrow a .\overrightarrow b = \sqrt 6 ,$

$\Rightarrow \overrightarrow a .\overrightarrow b = \left| {\overrightarrow a } \right|.\left| {\overrightarrow b } \right|\cos \theta \Rightarrow \sqrt 6$

$ = 2\sqrt 3 \cos \theta$

$\Rightarrow \cos \theta = \frac{1}{{\sqrt 2 }} \Rightarrow \theta = \frac{\pi }{4} $

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

Given two independent events A and B such that P(A) = 0.3 and P(B) = 0.6. Find
$\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)$
→
Write a unit vector in the direction of $\vec{\text{b}}=2\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}}$.
→
If $\text{A}=\begin{bmatrix}2&1&4\\4&1&5 \end{bmatrix}$ and $\text{B}=\begin{bmatrix}3&-1\\2&2\\1&3\end{bmatrix}.$ Write the order of $AB$ and $BA.$
→
Evaluate the following integrals:
$\int\frac{\text{e}^\text{x}}{(1+\text{e}^\text{x})^2}\text{dx}$
→
Evaluate the following determinant:
$\begin{vmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta \end{vmatrix}$
→
Find the position vector of the min-point of the line segment AB, where A is the point (3, 4, -2) and B is the point (1, 2, 4).
→
Which of the following functions from $A$ to $B$ are one$-$one and onto? $f_2 = \{(2, a), (3, b), (4, c)\}; A = \{2, 3, 4\}, B = \{a, b, c\}$
→
If $\vec{\text{a}}=\hat{\text{i}}+\hat{\text{j}},\ \vec{\text{b}}=\hat{\text{j}}+\hat{\text{k}},\ \vec{\text{c}}=\hat{\text{k}}+\hat{\text{i}}$, find the unit vector in the direction of $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}$.
→
Differentiate w.r.t. x the function in Exercise:
$\cos(\text{a}\cos\text{x}+\text{b}\sin\text{x}),\ $ for some constant a and b.
→
Write the smallest reflexive relation on set $A = \{1, 2, 3, 4\}.$
→