Download App

STD 12 - 10. vector algebra — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 10. vector algebra1 Mark
MCQ
If the vector $i + j + k$ makes angles $\alpha ,\,\beta ,\,\gamma $ with vectors $i,\,j,k$ respectively, then
  • A
    $\alpha = \beta \ne \gamma $
  • B
    $\alpha = \gamma \ne \beta $
  • C
    $\beta = \gamma \ne \alpha $
  • ✓
    $\alpha = \beta = \gamma $
✓

Answer

Correct option: D.
$\alpha = \beta = \gamma $
d
(d) Angle between $i + j + k$ and $i$ is equal to

${\cos ^{ - 1}}\left\{ {\frac{{(i + j + k)\,.\,i}}{{|i + j + k|\,\,|i|}}} \right\} \Rightarrow \alpha = {\cos ^{ - 1}}\left( {\frac{1}{{\sqrt 3 }}} \right)$

Similarly angle between $i + j + k$ and $j$ is $\beta = {\cos ^{ - 1}}\left( {\frac{1}{{\sqrt 3 }}} \right)$ and between $i + j + k$ and

$k$ is $\gamma = {\cos ^{ - 1}}\left( {\frac{1}{{\sqrt 3 }}} \right)\,.$

Hence $\alpha = \beta = \gamma .$

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 STD 12 - 10. vector algebra→STD 12 - 10. vector algebra — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

A function $f(x)$ satisfies $f\left( x \right) = f\left( {\frac{c}{x}} \right)$ for some real number $c\left( {c > 1} \right)$ and $\forall\, x > 0$. If $\int\limits_1^{\sqrt c } {\frac{{f\left( x \right)}}{x}} dx = 3$ , then the value of $\int\limits_1^c {\frac{{f\left( x \right)}}{x}} dx$ is
→
The system of equations  $-k x+3 y-14 z=25$  $-15 x+4 y-k z=3$  $-4 x+y+3 z=4$  is consistent for all $k$ in the set
→
$\int\text{e}^{\text{x}}\{\text{f(x)}+\text{f}'(\text{x})\}\text{dx}=$
→
If $\text{A}+\text{B}+\text{C}=\pi,$ then the value of $\begin{vmatrix}\sin(\text{A}+\text{B}+\text{C})&\sin(\text{A}+\text{C})&\cos\text{C}\\-\sin\text{B}&0&\tan\text{A}\\\cos(\text{A}+\text{B})&\tan(\text{B}+\text{C})&0\end{vmatrix}$ is equal to:
→
$(2, -3, -1) 2x - 3y + 6z + 7 = 0:$
→
If $A$ is a square matrix of order $4$ and $B = AdjA$, where $|B| = 27$, then value of $|A^{-1}Adj(3AB)|$ is, (where $A^{-1}$ denotes inverse of matrix $A$ and $AdjA$ denotes adjoint of matrix $A$) -
→
Let $\text{f}:\text{R}-\Big\{\frac{3}{5}\Big\}\rightarrow\ \text{R}$ be defined by $\text{f(x)}=\frac{3\text{x}+2}{5\text{x}-3}.$ Then,
→
If three non-zero vectors are $a = {a_1}i + {a_2}j + {a_3}k,$ $b = {b_1}i + {b_2}j + {b_3}k$ and $c = {c_1}i + {c_2}j + {c_3}k.$ If  $c$ is the unit vector perpendicular to the vectors $a$  and $ b$  and the angle between $a$  and $b $ is $\frac{\pi }{6},$ then ${\left| {\,\begin{array}{*{20}{c}}{{a_1}}&{{a_2}}&{{a_3}}\\{{b_1}}&{{b_2}}&{{b_3}}\\{{c_1}}&{{c_2}}&{{c_3}}\end{array}\,} \right|^2}$ is equal to
→
If $\int_{-2}^3 x^2 d x=k \int_0^2 x^2 d x+\int_2^3 x^2 d x$, then the value of $k$ is
→
Let $\vec{a}=2 \hat{i}+3 \hat{j}+4 \hat{k}, \vec{b}=2 \hat{i}-2 \hat{j}-2 \hat{k}$ and $\overrightarrow{ c }=-\hat{ i }+4 \hat{ j }+3 \hat{ k }$. If $\overrightarrow{ d }$ is a vector perpendicular to both $\vec{b}$ and $\overrightarrow{ c }$ and $\overrightarrow{ a } \cdot \overrightarrow{ d }=18$, Then $|\overrightarrow{ a } \times \overrightarrow{ d }|^2$ is equal to $..........$.
→