30
MCQ (Single Correct Answer)
If the direction cosines of a line are $k, k$ and $k$, then
A
$k>0$
B
$0< k<1$
C
$k=1$
D
$k=\frac{1}{\sqrt{3}}$ or $-\frac{1}{\sqrt{3}}$
31
MCQ (Single Correct Answer)
The distance of the plane $\overrightarrow{\mathbf{r}}\left(\frac{2}{7} \hat{\mathbf{i}}+\frac{3}{7} \hat{\mathbf{j}}-\frac{6}{7} \hat{\mathbf{k}}\right)=1$ from the origin is
A
$1$
B
$7$
C
$\frac{1}{7}$
D
None of these
32
MCQ (Single Correct Answer)
The sine of the angle between the straight line $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ and the plane $2 x-2 y+z=5$ is
A
$\frac{10}{6 \sqrt{5}}$
B
$\frac{4}{5 \sqrt{2}}$
C
$\frac{2 \sqrt{3}}{5}$
D
$\frac{\sqrt{2}}{10}$
33
MCQ (Single Correct Answer)
The reflection of the point $(\alpha, \beta, \gamma)$ in the $X Y$-plane is
A
$(\alpha, \beta, 0)$
B
$(0,0, \gamma)$
C
$(-\alpha,-\beta, \gamma)$
D
$(\alpha, \beta,-\gamma)$
34
MCQ (Single Correct Answer)
The area of the quadrilateral $A B C D$ where $A(0,4,1)$, $B(2,3,-1), C(4,5,0)$, and $D(2,6,2)$ is equal to
A
9 sq units
B
18 sq units
C
27 sq units
D
81 sq units