Write the projection of r =3 i -4 j +12 k on the coordinate axes. - Vidyadip

Question

Write the projection of $\vec{\text{r}}=3\hat{\text{i}}-4\hat{\text{j}}+12\hat{\text{k}}$ on the coordinate axes.

✓

Answer

We have
$\vec{\text{r}}=3\hat{\text{i}}-4\hat{\text{j}}+12\hat{\text{k}}$
Projection of $\vec{\text{r}}$ on x-axis $=\frac{\vec{\text{r}}.\hat{\text{i}}}{|\hat{\text{i}}|}=\frac{3}{1}=3$
Projection of $\vec{\text{r}}$ on y-axis $=\frac{\vec{\text{r}}.\hat{\text{j}}}{|\hat{\text{j}}|}=\frac{-4}{1}=-4$
Projection of $\vec{\text{r}}$ on z-axis $=\frac{\vec{\text{r}}.\hat{\text{k}}}{|\hat{\text{k}}|}=\frac{12}{1}=12$

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 "Solve the Following Question.(2 Marks)" from Scalar Or Dot Product→Scalar Or Dot Product — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Evaluate the following : $\int \frac{1}{\sqrt{3 x+1}-\sqrt{3 x-5}} \cdot d x$

Find the equation of the plane passing through the following point:
(2, 3, 4), (-3, 5, 1) and (4, -1, 2)

A fair coin is tossed five times. Find the probability that it shows exactly three times head.

Determine whether or not the definition of * given below gives a binary operation. In the event that * is not a binary operation give justification of this.
On R, define by $a^* b=a b^2$.
Here, $Z ^{+}$denotes the set of all non-negative integers.

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.

Show that $\text{f}(\text{x})=\tan\text{x}$ is an increasing function on $\Big(\frac{-\pi}{2},\frac{\pi}{2}\Big).$

If points $A(5,5, \lambda), B(-1,3,2)$ and $C(-4,2,-2)$ are collinear, then find the value of $\lambda$.

Write a vector of magnitude 12 units which makes 45º angle with x-axis, 60º angle with y-axis and an obtuse angle with z-axis.

If A is a square matrix of order $3$ such that |A| = 5, write the value of $|adj A|$.

Evaluate the following:

$\int_0^1\left(\frac{1}{1+x^2}\right) \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) d x$