Download App

Scalar Or Dot Product — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsScalar Or Dot Product2 Marks
Question
If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are three mutually perpendicular unit vectors, then prove that $\big|\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}\big|=\sqrt{3}$
✓

Answer

Given that $\vec{\text{a}},\vec{\text{b}}$ and $\vec{\text{c}}$ are unit vectors.
So, $\big|\vec{\text{a}}\big|=1,\Big|\vec{\text{b}}\big|=1$ and $\big|\vec{\text{c}}\big|=1$
Since they are mutually perpendicular,
$\vec{\text{a}}.\vec{\text{b}}=\vec{\text{b}}.\vec{\text{c}}=\vec{\text{c}}.\vec{\text{a}}=0$
Now,
$\big|\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}\big|^2=|\vec{\text{a}}|^2+\big|\vec{\text{b}}\big|^2+|\vec{\text{c}}|+2\vec{\text{a}}.\vec{\text{b}}+2\vec{{\text{b}}}.\vec{\text{c}}+2\vec{\text{c}}.\vec{\text{a}}$
$=1+1+1+0+0+0$
$=3$
$\therefore\big|\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}\big|=\sqrt{3}$

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

If $A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$ and $A X=I$, then find $X$ by using elementary transformations.
→
Let $\text{A}=\begin{bmatrix}2&4\\3&2\end{bmatrix},\text{B}=\begin{bmatrix}1&3\\-2&5\end{bmatrix}$ and $\text{C}=\begin{bmatrix}-2&5\\3&4\end{bmatrix}.$ Find each of the following:
$3\text{A}-\text{C}$
→
Prove The Following : $\int \frac{1}{x^2-a^2} \cdot d x=\frac{1}{2 a} \log \left(\frac{x-a}{x+a}\right)+c$
→
The radius of a circle is increasing at the rate of 0.5cm/ sec. Find the rate of increase of its circumference.
→
Check whether conditions of Rolle's theorem are satisfied by the following functions. : $f(x)=x^2-2 x+3, x \in[1,4]$
→
Evaluate : $\int_0^{\frac{\pi}{4}} \sec ^4 x d x$
→
Evalute the following integrals:
$\int\frac{1}{\text{x}\log\text{x}}\text{dx}$
→
Evaluate the following:
$\cot^{-1}\Big(\cot\frac{19\pi}{6}\Big)$
→
The probability distribution of a discrete random variable $X$ is :
$X =x$12345
$P ( X =x)$$k$$2k$$3k$$4k$$5k$

Find $( X \leq 4$ )
→
If the tangent to a curve at a point (x, y) is equally inclined to the co-ordinates axes then write the value of $\frac{\text{dy}}{\text{dx}}.$
→