Download App

VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA1 Mark
MCQ
If $\vec{a}$ is a nonzero vector of magnitude 'a' and $\lambda$ a nonzero scalar, then $\lambda\ \vec{a}$ is unit vector if
  • A
    $\lambda=1$
  • B
    $\lambda=-1$
  • C
    $a=\big|\lambda\big|$
  • ✓
    $a=1/\big|\lambda\big|$
✓

Answer

Correct option: D.
$a=1/\big|\lambda\big|$
Given: $ \vec{a}$ is a non-zero vector of magnitude a $ \Rightarrow\ \ \ |\vec{a}|=1$
Also given $\lambda\neq0\ \text{and}\ \lambda\vec{a}$ is a unit vector.
$\Rightarrow\ \ |\lambda\vec{a}|=1\ \Rightarrow\ \ |\lambda|\big|\vec{a}\big|=1$
$\Rightarrow\ \ \ \ \ \ |\lambda|a=1\ \ \Rightarrow\ \ a=\frac{1}{|\lambda|}$
Therefore, option (D) is correct.

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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\sin\text{y}=\text{x}\cos(\text{a}+\text{y}),$ then $\frac{\text{dy}}{\text{dx}}$ is equal to :
→
The vector equation r = i − 2j − k + t(6j − k) represents a straight line passing through the points:
→
If $p = \frac{{b \times c}}{{[a\,b\,c]}},\,\,q = \frac{{c \times a}}{{[a\,b\,c]}},\,\,r = \frac{{a \times b}}{{[a\,b\,c]}},\,\,$where $a, b, c $ are three non-coplanar vectors, then the value of $(a + b + c)\,.\,(p + q + r)$ is given by
→
Given $ABC$ is an equilateral triangle of side length $1$ unit and $P$ be any arbitrary point on the circumcircle of triangle $ABC,$ then $|\vec PA|^2+|\vec PB|^2+|\vec PC|^2$ is equal to 
→
Choose the correct answer from the given four options.If $\text{P}(\text{A})=0.4,\text{P}(\text{B})=0.8$ and $\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)=0.6,$ then $\text{P}(\text{A}\cup\text{B})$ is equal to:
→
If $f(a + b - x) = f(x),$ then $\int_a^b {x\,f(x)\,dx = } $
→
Which of the following are true?
→
The value of $\int \cos ^2 x\ d x$ will be
→
Let $\alpha$ and $\beta$ be the distinct roots of the equation $x^2+x-1=0$. Consider the set $T=\{1, \alpha, \beta\}$. For a $3 \times 3$ matrix $M=\left(a_{\ell}\right) 3 \times 3_3$, define $R_l=a_{l 1}+a_{l 2}+a_\beta$ and $C_j=a_{1 j}+a_{2 l}+a_{3 j}$ for $i=1,2,3$ and $j=1,2,3$

Match each entry in $List-I$ to the correct entry in $List-II$.

$List-I$ $List-II$
($P$) The number of matrices $M=\left(a_{i j}\right)_3 \times 3$ with all entries in $T$ such that $R_i=C_j=0$ for all $i, j$ is ($1$) ($1$)
($Q$) The number of symmetric matrices $M=\left(a_{i j}\right) 3 \times 3$ with all entries in $T$ such that $C_j=0$ for all $j$ is ($2$) ($2$)
($R$) Let $M=\left(a_{i j}\right) 3 \times 3$ be a skew symmetric matrix such that $a_{i j} \in T$ for $i>j$. Then the number of elements in the set $\left\{\left(\begin{array}{l}x \\ y \\ z\end{array}\right): x, y \cdot z \in R, M\left(\begin{array}{l}x \\ y \\ z\end{array}\right)=\left(\begin{array}{c}a_{12} \\ 0 \\ -a_{23}\end{array}\right)\right\}$ is is ($3$) Infinite
($S$) Let $M=\left(a_{i j}\right)_3 \times 3$ be a matrix with all entries in $T$ such that $R_i=0$ for all $i$. Then the absolute value of the determinant of $M$ is ($4$) ($6$)
  ($5$) ($0$)

The correct option is

→
If ${\cos ^{ - 1}}x - {\cos ^{ - 1}}\frac{y}{2} = \alpha $, then $4{x^2} - 4xy\cos \alpha + {y^2}$ is equal to
→