Let the vectors a ; and b be such that | a | = 3 ; and ; | b | = … - Vidyadip

Question

Let the vectors $\vec a\;$ and $\vec b$ be such that $\left| {\vec a} \right| = 3\;$ and $\;\left| b \right| = \frac{{\sqrt 2 }}{3},\;$ then $\;\vec a \times \vec b$ is a unit vector if the angle between $\vec a\;$ and $\vec b\;$ is

✓

Answer

It is given that $\overrightarrow{a}\times \overrightarrow{b}$ is a unit vector, then:
$\Rightarrow |\vec a\times \vec b|=1\Rightarrow |\vec a||\vec b|sin\theta =1$
$\Rightarrow 3.\frac{\sqrt2}{3}sin\theta=1\Rightarrow sin\theta =\frac{1}{\sqrt2}\Rightarrow \theta =\frac{\pi}{4}$

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 "1 Marks Question" from Vector Algebra→Vector Algebra — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Given an example of:
A diagonal matrix which is not scalar.

A relation $R$ is defined as $A R B \Leftrightarrow A$ is subset of $B$ is sets of set S . Is this relation R will anti symmetric?

Evaluate the following:
$\cot^{-1}\Big(\cot\frac{\pi}{3}\Big)$

If a matrix has 5 elements, write all possible orders it can have.

Find:
$\int \frac{\sin^{2} \text{x} - \cos^{2} \text{x}}{\sin \text{x} \cos \text{x}} \text{dx}$

Find the scalar components of the vector $\overrightarrow{\text{AB}}$ with initial point A(2, 1) and terminal point B(- 5, 7).

Integrate the function: $\frac{x \cos ^{-1} x}{\sqrt{1-x^{2}}}$

if A is a $3\times3$ matrix and $\text{|3A| = K|A|,}$ then write the value of k.

For what value of x, is the following matrix singular?
$\begin{vmatrix} \text{3-2x} & \text{x + 1} \\ 2 & 4 \\ \end{vmatrix}$.

Evaluate $\int_0^1 \frac{\left(x^2-x\right)}{\sqrt{x}} d x$.