Download App

Scalar Or Dot Product — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSScalar Or Dot Product2 Marks
Question
Find the angle betwwen two vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ if$|\vec{\text{a}}|=3,\big|\vec{\text{b}}\big|=3$ and $\vec{\text{a}}.\vec{\text{b}}=1$
✓

Answer

Let the angle between $\vec{\text{a}}$ and $\vec{\text{b}}$ is $\theta,$ then
$\cos\theta=\frac{\vec{\text{a}}.\vec{\text{b}}}{|\vec{\text{a}}|\big|\vec{\text{b}}\big|}$
$=\frac{1}{3.3}$
$\cos\theta=\frac{1}{9}$
$\theta=\cos^{-1}\big(\frac{1}{9}\big)$

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 Scalar Or Dot Product→Scalar Or Dot Product — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the second order derivatives of the function given in Exercise:
$\text{e}^{6\text{x}}\cos3\text{x}$
→
Prove that the determinant $\begin{vmatrix}x&\sin\theta&\cos\theta\\-\sin\theta&-x&1\\\cos\theta&1&x\end{vmatrix}$ is independent of θ.
→
Find the equation of the line joining A (1, 3) and B (0, 0) using determinants and find k if D (k, 0) is a point such that area of $\Delta ABD$ is 3 square units.
→
Find a vector in the direction of $\vec{\text{a}}=2\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}$, which has magnitude of 6 units.
→
Find the equation of the curve which passes through the point (3, -4) and has slope $\frac{2\text{y}}{\text{x}}$ at any point (x, y) on it.
→
Let the vectors $\vec{a},\vec{b},\vec{c}$ be given as $a_{1}\hat{i}+a_{2}\hat{j}+a_{3}\hat{k},\ b_{1}\hat{i}+b_{2}\hat{j}+b_{3}\hat{k},$ $c_{1}\hat{i}+c_{2}\hat{j}+c_{3}\hat{k}.$ Then show that  $\vec{a}\times(\vec{b}+\vec{c})=\vec{a}\times\vec{b}+\vec{a}\times\vec{c}.$
→
Find the values of $x$ and $y$ if.$\begin{bmatrix}\text{x}+10&\text{y}^2+2\text{y}\\0&-4\end{bmatrix}=\begin{bmatrix}3\text{x}+4&3\\0&\text{y}^2-5\text{y}\end{bmatrix}$
→
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 $
→
$F = \{(a, 2), (b, 1), (c, 1)\}.$
→
A bag contains 8 marbles of which 3 are blue and 5 are red. One marble is drawn at random, its cooler is noted and the marble is replaced in the bag. A marble is again drawn from the bag and its colour is noted. Find the probability that the marble will be,
Blue and red in any order.
→