Find the angle between two vectors i - 2 j + 3 k and 3 i - 2 j + … - Vidyadip

Question

Find the angle between two vectors $\hat i - 2\hat j + 3\hat k$ and $3\hat i - 2\hat j + \hat k\;$

✓

Answer

$\overrightarrow a = \widehat i - 2\widehat j + 3\widehat k,\overrightarrow b = 3\widehat i - 2\widehat j + \widehat k \Rightarrow \left| {\overrightarrow a } \right| = \sqrt {14} ,\left| {\overrightarrow b } \right| = \sqrt {14} ,\overrightarrow a .\overrightarrow b = 10, $

$ \Rightarrow \frac{{\overrightarrow a .\overrightarrow b }}{{\left| {\overrightarrow a } \right|\left| {\overrightarrow b } \right|}} = \cos \theta \Rightarrow \frac{{10}}{{14}} = \cos \theta $

$\Rightarrow \cos \theta = \frac{5}{7} \Rightarrow \theta = {\cos ^{ - 1}}\frac{5}{7} \\\\\\ $

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 "3 Marks Question" 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

Integrate the rational function $\frac{2 x}{x^{2}+3 x+2}$

Evaluate the following integrals:$\int\text{x}^2\sin^2\text{x dx}$

A fair die is tossed twice. If the number appearing on the top is less than 3, it is success. Find the probability distribution of number of successes.

Evaluate $\triangle=\begin{vmatrix}0&\sin\alpha&-\cos\alpha\\-\sin\alpha&0&\sin\beta\\\cos\alpha&-\sin\beta&0 \end{vmatrix}$

Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem.$\text{f}(\text{x})=\sin\text{x}-\sin2\text{x}-\text{x}\text{ on }[0,\pi]$

In a family, the husband tells a lie in 30% cases and the wife in 35% cases. Find the probability that both contradict each other on the same fact.

Prove that $\cot^{-1}\bigg(\frac{\sqrt{1 +\sin\text{x}} + \sqrt{1 -\sin\text{x}}}{\sqrt{1 + \sin\text{x}} - \sqrt{1 - \sin\text{x}}} \bigg)= \frac{\text{x}}{2}; \text{x}\in\bigg(0,\frac{\pi}{4}\bigg).$

If the coordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7), (-4, 3, -6) and (2, 9, 2) respectively, then find the angle between the lines AB and CD.

Differentiate the following functions with respect to x:
$\tan(\text{x}^\circ+45^\circ)$

A factory has two machines $A$ and $B.$ Past records show that the machine $A$ produced $60\%$ of the items of output and machine $B$ produced $40\%$ of the items. Further $2\%$ of the items produced by machine $A$ were defective and $1\%$ produced by machine $B$ were defective. If an item is drawn at random, what is the probability that it is defective?