Download App

11. three dimension geometry — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths11. three dimension geometry1 Mark
MCQ
The angle between two diagonals of a cube will be
  • A
    ${\sin ^{ - 1}}1/3$
  • ✓
    ${\cos ^{ - 1}}1/3$
  • C
    Variable
  • D
    None of these
✓

Answer

Correct option: B.
${\cos ^{ - 1}}1/3$
b
(b) Let the cube be of side $'a'$

$O\,(0,\,\,0,\,\,0),\,\,D\,(a,\,\,a,\,\,a),\,\,B\,(0,\,\,a,\,\,0),\,\,G\,(a,\,\,0,\,\,a)$

Then equation of $OD$ and $BG$ are $\frac{x}{a} = \frac{y}{a} = \frac{z}{a}$ and

$\frac{x}{a} = \frac{{y - a}}{{ - a}} = \frac{z}{a}$ respectively.

Hence, angle between $OD$ and $BG$ is

${\cos ^{ - 1}}\left( {\frac{{{a^2} - {a^2} + {a^2}}}{{\sqrt {3{a^2}} .\,\sqrt {3{a^2}} }}} \right) = {\cos ^{ - 1}}\,\left( {\frac{1}{3}} \right)$.

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 11. three dimension geometry→11. three dimension geometry — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The value of the integral $\int\limits_0^1 {x\,{{\cot }^{ - 1}}\,\left( {1 - {x^2} + {x^4}} \right)} dx$ is
→
The value of $\int_{\,0}^{\,\pi /2} {\frac{{{2^{\sin x}}}}{{{2^{\sin x}} + {2^{\cos x}}}}dx} $ is
→
If $\begin{vmatrix}2\text{x}&5\\8&\text{x}\end{vmatrix}=\begin{vmatrix}6&-2\\7&3\end{vmatrix},$ then x =
  1. $3$
  2. $\pm3$
  3. $\pm6$
  4. $6$
→
Evaluate $\begin{bmatrix}8\text{x}+1&2\text{x}-2\\\text{x}^2-1&3\text{x}+5\end{bmatrix}$ is:
  1. -2x3 - 26x2 + 45x + 3
  2. -2x3 + 26x2 + 45x + 3
  3. -2x3 + 26x2 + 45x - 3
  4. -2x3 - 26x2- 45x + 3
→
Consider the piecewise defined functionf $f(x) = \left[ \begin{gathered}   \hfill \\   \hfill \\   \hfill \\   \hfill \\ \end{gathered}  \right.$$\begin{gathered}  \sqrt { - x}  & if\,\,\,\,\,\,\,\,\,\,x < 0 \hfill \\    \hfill \\  \,\,\,\,\,\,0 & if\,\,0 \leqslant x \leqslant 4 \hfill \\   \hfill \\  x - 4 & if\,\,\,\,\,\,\,\,\,\,x > 4 \hfill \\  \end{gathered} $ choose the answer which best describes the continuity of this function
→
If non-zero real numbers $b$ and $c$ are such that $min \,f\left( x \right) > \max \,g\left( x \right)$, where $f\left( x \right) = {x^2} + 2bx + 2{c^2}$  and $g\left( x \right) = {-x^2} - 2cx + {b^2}$$\left( {x \in R} \right)$; then $\left| {\frac{c}{b}} \right|$ lies in the interval
→
The transpose of a square matrix is a?
  1. rectangular matrix
  2. diagonal matrix
  3. square matrix
  4. scaler matrix
→
$\text{Let A}=\begin{bmatrix}1&\sin\theta&1\\-\sin\theta&1&\sin\theta\\-1&-\sin\theta&1\end{bmatrix},$ where $0\leq\theta\leq2\pi.$ Then
  1. Det (A) = 0
  2. Det (A) $\in$ (2, $\infty$)
  3. Det (A) $\in$ (2, 4)
  4. Det (A) $\in$ [2, 4]
→
The solution set of the inequality $3 x+5 y<4$ is
→
If $\cos^{-1}\text{x}>\sin^{-1}\text{x},$ then:
  1. $\frac{1}{\sqrt2}<\text{x}\leq1$
  2. $0\leq\text{x}\leq\frac{1}{\sqrt2}$
  3. $-1\leq\text{x}<\frac{1}{\sqrt2}$
  4. $\text{x}>0$
→