Download App

VECTOR ALGEBRA — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVECTOR ALGEBRA1 Mark
Question
If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}} $ are three non-coplanar mutually perpendicular unit vectors, then $\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big],$ is:
  1. $\pm 1$
  2. $0$
  3. $-2$
  4. $2$
✓

Answer

  1. $\pm1$
Solution:
We have
$\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big]$
$=\big(\vec{\text{a}}\times\vec{\text{b}}\big).\vec{\text{c}}$
$=\big|\vec{\text{a}}\times\vec{\text{b}}\big|\big|\vec{\text{c}}\big|\cos0^\circ$ or $\big|\vec{\text{a}}\times{\vec{\text{b}}}\big|\big|\vec{\text{c}}\big|\cos180^\circ$ $\big(\therefore\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are perpendicular to each other$)$
$=\big|\vec{\text{a}}\times\vec{\text{b}}\big|$ or $-\big|\vec{\text{a}}\times\vec{\text{b}}\big|$  $\big(\therefore\big|\vec{\text{c}}\big|=1,\cos0^\circ=1\text{ and }\cos180^\circ=-1\big)$  $$
$=\big|\vec{\text{a}}\big|\big|\vec{\text{b}}\big|\sin90^\circ$ or $-\big|\text{a}\big|\big|\vec{\text{b}}\big|\sin90$  $\big(\therefore\vec{\text{a}} \text{ is perpendicular to }\vec{\text{b}})$ 
$=1 \text{ or }-1$ $\big(\therefore\big|\vec{\text{a}}\big|=1 \text{ and }\big|\vec{\text{b}}\big|=1\big)$ $$
$=\pm1$

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 "M.C.Q (1 Marks)" 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 $\text{a},\text{b},\text{c}\in+\text{R}$ such that $\lambda\text{ abc}$ is the minimum value of $a(b^2 + c^2) + b(c^2 + a^2) + c(a^2 + b^2),$ then $\lambda=$
→
If $\vec{a}$ is a nonzero vector of magnitude ' $a$ ' and $\lambda$ a nonzero scalar, then $\lambda \vec{a}$ is unit vector if :
→
Choose the correct option from given four options:
$\int\tan^{-1}\sqrt{\text{x}}\text{ dx}$ is equal to:
  1. $(\text{x}+1)\tan^{-1}\sqrt{\text{x}}-\sqrt{\text{x}}+\text{C}$
  2. $\text{x}\tan^{-1}\sqrt{\text{x}}-\sqrt{\text{x}}+\text{C}$
  3. $\sqrt{\text{x}}-\text{x}\tan^{-1}\sqrt{\text{x}}+\text{C}$
  4. $\sqrt{\text{x}}-(\text{x}+1)\tan^{-1}\sqrt{\text{x}}+\text{C}$
→
The lines $\frac{\text{x}}{1}=\frac{\text{y}}{2}=\frac{\text{z}}{3}$ and $\frac{\text{x}-1}{-2}=\frac{\text{y}-2}{-4}=\frac{\text{z}-3}{-6}$ are:
→
If the diraction ratios of a line are proportional to 1, -3, 2, then its diraction cosines are:
→
A fair die is tossed eight times. The probability that a third six is observed in the eight throw is:
  1. $\frac{\text{ }^7\text{C}_2\times5^5}{6^7}$
  2. $\frac{\text{ }^7\text{C}_2\times5^5}{6^8}$
  3. $\frac{\text{ }^7\text{C}_2\times5^5}{6^6}$
  4. $\text{None of these}$
→
Write the direction cosines of a line parallel to the line $\frac{3-x}{3}=\frac{y+2}{-2}=\frac{z+2}{6}$.
→
Find the degree of the differential equation:
$\Big(1+\frac{\text{dx}}{\text{dy}}\Big)^3=\Big(\frac{\text{dy}}{\text{dx}}\Big)^2$
  1. 0
  2. 1
  3. 2
  4. 3
→
Which of the following functions from $\text{A}=\{\text{x}\in\text{R}:-1\leq\text{x}\leq1\}$ to itself are bijections?
  1. $\text{f(x)}=|\text{x}|$
  2. $\text{f(x)}=\sin\frac{\pi\text{x}}{2}$
  3. $\text{f(x)}=\sin\frac{\pi\text{x}}{4}$
  4. $\text{None of these}$
→
If $f(x)=x+1$, find $\frac{d}{d x}(f o f)(x)$.
→