Download App

Scalar Or Dot Product — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSScalar Or Dot Product1 Mark
Question
The vector $(\cos\text{a}\cos\beta)\hat{\text{i}}+(\cos\text{a}\sin\beta)\hat{\text{j}}+(\sin\text{a})\hat{\text{k}}$is a:
  1. Null vector
  2. Unit vector
  3. Constant vector
  4. None of these
✓

Answer

  1. Unit vector
Solution:
Let $\vec{\text{a}}=(\cos\text{a}\cos\beta)\hat{\text{i}}+(\cos\text{a}\sin\beta)\hat{\text{j}}+(\sin\text{a})\hat{\text{k}}$
$|\vec{\text{a}}|=\sqrt{\cos^2\text{a}\cos^2\beta+\cos^2\text{a}\sin^2\beta+\sin^2\text{a}}$
$=\sqrt{\cos^2\text{a}(\cos^2\beta+\sin^2\beta)+\sin^2\text{a}}$
$=\sqrt{\cos^2\text{a}(1)+\sin^2\text{a}}$
$=\sqrt{\cos^2\text{a}+\sin^2\text{a}}$
$=\sqrt{1}$
$=1$
So, $\vec{\text{a}}$ is a unit vector.

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 Scalar Or Dot Product→Scalar Or Dot Product — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Maximize Z = 11 x + 8y subject to $\text{x}\leq4,\text{y}\leq6,\text{x}+\text{y}\leq6,\text{x}\geq0,\text{y}\geq0.$
→
Let f(x) = (x + |x|) |x|. Then, for all x:
  1. f is continuous.
  2. f is differentiable for some x
  3. f' is continuous.
  4. f'' is continuous.
→
Time period is a:
  1. Vector quantity
  2. Scalar quantity
  3. Neither scalar nor vector
  4. None of these
→
Let * be a binary operation on R defined by a * b = ab + 1. Then, * is:
  1. Commutative but not associative.
  2. Associative but not commutative.
  3. Neither commutative nor associative.
  4. Both commutative and associative.
→
If $A=\left[\begin{array}{ll}x & 0 \\ 1 & 1\end{array}\right]$ and $B=\left[\begin{array}{cc}4 & 0 \\ -1 & 1\end{array}\right]$, then value of $x$ for which $A^2=B$ is
→
If $\sin^{-1}\Big(\frac{\text{x}^2-\text{y}^2}{\text{x}^2+\text{y}^2}\Big)=\log\text{a}$ then $\frac{\text{dy}}{\text{dx}}$ is equal to:
  1. $\frac{\text{x}^2-\text{y}^2}{\text{x}^2+\text{y}^2}$
  2. $\frac{\text{y}}{\text{x}}$
  3. $\frac{\text{x}}{\text{y}}$
  4. $\text{None of these.}$
→
The point on the curve $9y^2 = x^3,$ where the normal to the curve makes equal intercepts with the axes is:
→
The area of the region bounded by the parabola $y = x^2$ and $y = |x|$ is$:$
→
The positive integral solution of the equation$\tan^{-1}\text{x}+\cos^{-1}\frac{\text{y}}{\sqrt{1+\text{y}^2}}=\sin^{-1}\frac{3}{\sqrt{10}}$ is:
  1. x = 1, y = 2
  2. x = 2, y = 1
  3. x = 3, y = 2
  4. x = -2, y = -1
→
The vector $(\cos\text{a}\cos\beta)\hat{\text{i}}+(\cos\text{a}\sin\beta)\hat{\text{j}}+(\sin\text{a})\hat{\text{k}}$is a:
  1. Null vector
  2. Unit vector
  3. Constant vector
  4. None of these
→