Download App

10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
The direction cosines of the vector $3i - 4j + 5k$ are
  • A
    $\frac{3}{5},\,\frac{{ - 4}}{5},\frac{1}{5}$
  • ✓
    $\frac{3}{{5\sqrt 2 }},\,\frac{{ - 4}}{{5\sqrt 2 }},\frac{1}{{\sqrt 2 }}$
  • C
    $\frac{3}{{\sqrt 2 }},\,\frac{{ - 4}}{{\sqrt 2 }},\,\frac{1}{{\sqrt 2 }}$
  • D
    $\frac{3}{{5\sqrt 2 }},\,\,\frac{4}{{5\sqrt 2 }},\,\frac{1}{{\sqrt 2 }}$
✓

Answer

Correct option: B.
$\frac{3}{{5\sqrt 2 }},\,\frac{{ - 4}}{{5\sqrt 2 }},\frac{1}{{\sqrt 2 }}$
b
(b) Vector$\overrightarrow A  = 3i - 4j + 5k$ We know that direction cosines of  $\overrightarrow A $

$ = \frac{3}{{\sqrt {{3^2} + {4^2} + {5^2}} }},\,\frac{{ - 4}}{{\sqrt {{3^2} + {4^2} + {5^2}} }},\,\frac{5}{{\sqrt {{3^2} + {4^2} + {5^2}} }}$

$ = \frac{3}{{5\sqrt 2 }},\,\frac{{ - 4}}{{5\sqrt 2 }},\,\frac{1}{{\sqrt 2 }}$.

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 10. vector algebra→10. 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

$\int_{}^{} {\frac{{{x^2}{{\tan }^{ - 1}}{x^3}}}{{1 + {x^6}}}\;dx} $ is equal to
→
If $x + y = 16$ and ${x^2} + {y^2}$ is minimum, then the values of $x$ and $y$ are
→
If the lines $\text{ x - }\frac{2}{1} =\text{y}-\frac{2}{1} =\text{z}-\frac{4}{\text{k}} $ and $\text{x}-\frac{1}{\text{k}} = \text{y}-\frac{4}{2} = \text{z}-\frac{5}{1} $ are coplanar, then k can have:
→
Choose the correct answer from given four options in each of the Exercise:
The value of $\begin{vmatrix}\text{a}-\text{b}&\text{b}+\text{c}&\text{a}\\\text{b}-\text{a}&\text{c}+\text{a}&\text{b}\\\text{c}-\text{a}&\text{a}+\text{b}&\text{c}\end{vmatrix}$ is:
  1. a3 + b3 + c3
  2. 3bc
  3. a3 + b3 + c3 - 3abc
  4. None of these.
→
Consider $f(x)=\left\{\begin{matrix}
tan^{-1}(\frac{\alpha x+\beta}{\gamma})\ \ \ x\in(0,\frac{1}{2}) and   \\0  \ \ \  \ \ \ \ x=\frac{1}{2}
 and \\ ln(\beta x^2 +2) \ \ \ \ \ \ x\in(\frac{1}{2},1) 
and\end{matrix}\right.$  . If $f(x)$ continuous and derivable in its domain then the value of $\alpha + \beta + \gamma$ is-
→
If $f(x)=\int_{0}^{x} t \sin t \,d t,$ then $f^{\prime}(x)$ is
→
The solution of the differential equation $\frac{{{d^2}y}}{{d{x^2}}} = - \frac{1}{{{x^2}}}$ is
→
Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b for all a, b ∈ T. Then, R is:
  1. Reflexive but not symmetric.
  2. Transitive but not symmetric.
  3. Equivalence.
  4. None of these.
→
Let $f(x)=\int_0^x g(t) \log _e\left(\frac{1-t}{1+t}\right) d t$, where $g$ is a continuous odd function. If $\int_{-\pi / 2}^{\pi / 2}\left(f(x)+\frac{x^2 \cos x}{1+e^x}\right) d x=\left(\frac{\pi}{\alpha}\right)^2-\alpha$, then $\alpha$ is equal to..............
→
The value of $\int_{ - a}^a {\frac{1}{{x + {x^3}}}dx} $ is
→