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
35
MCQ (Single Correct Answer)
The locus represented by $x y+y z=0$ is
A
a pair of perpendicular lines
B
a pair of parallel lines
C
a pair of parallel planes
D
a pair of perpendicular planes
36
MCQ (Single Correct Answer)
If the plane $2 x-3 y+6 z-11=0$ makes an angle $\sin ^{-1} \alpha$ with $X$-axis, then the value of $\alpha$ is
A
$\frac{\sqrt{3}}{2}$
B
$\frac{\sqrt{2}}{3}$
C
$\frac{2}{7}$
D
$\frac{3}{7}$
37
If a plane passes through the points $(2,0,0)(0,3,0)$ and $(0,0,4)$ the equation of plane is ................ .
Explanation
We know that, equation of a the plane that cut the coordinate axes at $(a, 0,0)(0, b, 0)$ and $(0,0, c)$ is $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$.
Hence, the equation of plane passes through the points $(2,0,0),(0,3,0)$ and $(0,0,4)$ is $\frac{x}{2}+\frac{y}{3}+\frac{z}{4}=1$.