Download App

APPLICATION OF DERIVATIVES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAPPLICATION OF DERIVATIVES1 Mark
Question
If $\hat{\text{a}}, \hat{\text{b}}$ and $\hat{\text{c}}$are mutually perpendicular unit vectors, then find the value of $|\hat{2\text{a}} + \hat{\text{b}} + \hat{\text{c}}|.$
✓

Answer

$|2\hat{\text{a}} + \hat{\text{b}} + \hat{\text{c}}|^{2} = (2\hat{\text{a}})^{2} + (\hat{\text{b}})^{2} + (\hat{\text{c}})^{2} +2(2\hat{\text{a}}. \hat{\text{b}} + \hat{\text{b}}. \hat{\text{c}} + \hat{\text{c}}. 2\hat{\text{a}})$
$\therefore|2\hat{\text{a}} + \hat{\text{b}} + \hat{\text{c}}| = \sqrt{6}$

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 APPLICATION OF DERIVATIVES→APPLICATION OF DERIVATIVES — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Classify the following measures as scalars and vectors.
$20 m/s^2$
→
Find the scalar components of the vector $\overrightarrow{\text{AB}}$ with initial point A(2, 1) and terminal point B(- 5, 7).
→
Integrate the functions in Exercises:
$\frac{(1+\log\text{x})^2}{\text{x}}$
→
$\text{If }x \in \text{N and} \begin{bmatrix} \text{x + 3} & -2 \\ \text{-3x} & \text{2x} \\ \end{bmatrix} = 8, $ then find the value of $x.$
→
Probability of solving specific problem independently by A and B are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. If both try to solve the problem independently, find the probability that the problem is solved.
→
Write the degree of the differrntial equation $\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}\Big)^{2}+\Big(\frac{\text{dy}}{\text{dx}}\Big)^{2}=\text{x}\sin\Big(\frac{\text{dy}}{\text{dx}}\Big).$
→
Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\frac{\text{d}^2\text{y}}{\text{dx}^2}+3\Big(\frac{\text{dy}}{\text{dx}}\Big)^2=\text{x}^2\log\Big(\frac{\text{d}^2\text{y}}{\text{dx}^2}\Big)$
→
Show that the function given by $f(x) = e^{2x}$ is strictly increasing on R.
→
Write the order of the differential equation of all non-horizontal lines in a plane.
→
Discuss the continuity of the cosine, cosecant, secant and cotangent functions.
→