Question 11 Mark
Equation of y-axis is considered as:
- x = 0, y = 0.
- y = 0, z = 0.
- z = 0, x = 0.
- None of these.
Answer
View full question & answer→- z = 0, x = 0.
Solution:
On y-axis, x = 0 and z = 0
Hence, the correct option is (c).
13 questions · timed · auto-graded
Equation of y-axis is considered as:
Solution:
On y-axis, x = 0 and z = 0
Hence, the correct option is (c).
What is the length of foot of perpendicular drawn from the point P(3, 4, 5) on y-axis.
$\sqrt{41}$
$\sqrt{34}$
$5$
$\text{None of these.}$
Solution:
We know that, on the y-axis x = 0 and z = 0.
$\therefore$ Point $\text{A}\equiv(0,4,0)$
$\therefore\text{PA}=\sqrt{(0-3)^2+(4-4)^2+(0-5)^2}$
$=\sqrt{9+0+25}=\sqrt{34}$
A plane is parallel to yz-plane so it is perpendicular to:
Solution:
Any plane parallel to yz-plane, so it is perpendicular to x-axis.
Hence, the correct option is (a)
The distance of point P(3, 4, 5) from the yz-plane is:
Solution:
Given point is P(3, 4, 5)
$\therefore$ Distance of from yz-plane
$=\sqrt{(0-3)^2+(4-4)^2+(5-5)^2}$
$=\sqrt{9}=3\text{ units}$
Hence, the correct option is (a).
The point (-2, -3, -4) lies in the:
Solution:
The point (-2, -3, -4) lies in seventh octant.
Hence the correct option is (b).
L is the foot of the perpendicular drawn from a point P(3, 4, 5) on the xy-plane. The coordinates of point L are:
Solution:
We know that on the xy-plane, z = 0.
Hence, the coordinates of the points L are (3, 4, 0).
x-axis is the intersection of two planes:
Solution:
We know that on the xy and xz-planes, the line of intersection is x-axis.
Hence, the correct option is (a).
If a parallelopiped is formed by planes drawn through the points (5, 8, 10) and (3, 6, 8) parallel to the coordinate planes, then the length of diagonal of the parallelopiped is:
$2\sqrt{3}$
$3\sqrt{2}$
$\sqrt{2}$
$\sqrt{3}$
Solution:
Given parallelepiped passes through A(5, 8, 10) and B(3, 6, 8)
$\therefore$ Length of the diagonal,
$\text{AB}=\sqrt{(5-3)^2+(8-6)^2+(10-8)^2}$ $=\sqrt{4+4+4}=2\sqrt{3}$
The locus of a point for which x = 0 is:
Solution:
On the yz-plane, x = 0
Hence, the locus of the point is yz-plane.
So, the correct option is (b).
Distance of the point (3, 4, 5) from the origin (0, 0, 0) is:
$\sqrt{50}$
$3$
$4$
$5$
Solution:
Given point A(3, 4, 5) and the given O(0, 0, 0)
$\therefore\sqrt{(3-0)^2+(4-0)^2+(5-0)^2}$
$=\sqrt{9+16+25}=\sqrt{50}$
Hence, the correct is a.
The locus of a point for which y = 0, z = 0 is:
Solution:
We know that one equation of x-axis, y = 0, z = 0
Hence, the locus of the point is equation of x-axis.
So, the correct option is (a).
If the distance between the points (a, 0, 1) and (0, 1, 2) is 27, then the value of a is:
$5$
$\pm5$
$-5$
None of these.
Solution:
Given points are A(a, 0, 1) and B(0, 1, 2).
$\therefore\text{AB}=\sqrt{(\text{a}-0)^2+(0-1)^2+(1-2)^2}=\sqrt{27}$ (Given)
$\Rightarrow27=\text{a}^2+2\ \Rightarrow\text{a}^2=25\ \Rightarrow\text{a}=\pm5$
L is the foot of the perpendicular drawn from a point (3, 4, 5) on x-axis. The coordinates of L are:
Solution:
On the x-axis, y = 0 and z = 0.
Hence, the required coordinates are (3, 0, 0).