If a is a unit vector such that a i = j , find a . i . - Vidyadip

Question

If $\vec{\text{a}}$ is a unit vector such that $\vec{\text{a}}\times\hat{\text{i}}=\hat{\text{j}},$ find $\vec{\text{a}}.\hat{\text{i}}.$

✓

Answer

We know
$\hat{\text{k}}\times\hat{\text{i}}=\hat{\text{j}}\dots(1)$
Given: $\vec{\text{a}}\times\hat{\text{i}}=\hat{\text{j}}\dots(2)$
Comparing (1) and (2), we get
$\vec{\text{a}}=\hat{\text{k}}$
Now,
$\vec{\text{a}}.\hat{\text{i}}=\hat{\text{k}}.\hat{\text{i}}$
$=0$

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 $A=\left[\begin{array}{cc}2 & 3 \\ 1 & -4\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & -2 \\ -1 & 3\end{array}\right]$ then verify that $(A B)^{-1}=B^{-1} A^{-1}$

Let A = {a, b, c} and the relation R be defined on A as follows: R = {(a, a), (b, c), (a, b)}. Then, write minimum number of ordered pairs to be added in R to make it reflexive and transitive.

Write the coefficient a, b, c of which the value of the integral $\int\limits^3_{-3}(\text{ax}^2+\text{bx}+\text{c})\text{dx}$ is independent.

If $\text{A}=\begin{bmatrix}1\\2\\3\end{bmatrix},$ write $AA^T.$

Evaluate the following definite integrals:
$\int_{0}^\limits{\infty}\text{e}^{-\text{x}}\text{ dx}$

Evaluate the following:
$\cos^{-1}\Big\{\cos\Big(\frac{13\pi}{6}\Big)\Big\}$

Evaluate the definite integrals $\int\limits_0^1 {\left( {x{e^x} + \sin \frac{{\pi x}}{4}} \right)dx} $

An edge of a variable cube is increasing at the rate of $3 \ cm$ per second. How fast is the volume of the cube increasing when the edge is $10 \ cm$ long?

Show that $\left[\begin{array}{rr} {5} & {-1} \\ {6} & {7} \end{array}\right]\left[\begin{array}{ll} {2} & {1} \\ {3} & {4} \end{array}\right] \neq\left[\begin{array}{ll} {2} & {1} \\ {3} & {4} \end{array}\right]\left[\begin{array}{rr} {5} & {-1} \\ {6} & {7} \end{array}\right]$

Kamal and Monica appeared for an interview for two vacancies. The probability of Kamal's selection is $\frac{1}{3}$ and that of Monika's selection is $\frac{1}{5}$. Find the probability that.
At least one of them will be selected.