Sample QuestionsPART - 2 CH - 11 Introduction to Three Dimensional Geometry questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Points $(5,3,2),(3,2,5)$ and $(2,5,3)$ are vertices of which of the following triangle?
Answer: B.
View full solution →If a variable point P move such that $x=a$ and $y=b$ then its locus is given by :
- A
a plane parallel to XY - plane
- B
a line parallel to X - axis
- C
a line parallel to Y - axis
- ✓
a line parallel to Z- axis
Answer: D.
View full solution →The coordinates of a point which is in YZ - plane are :
- A
$(x, 0, z)$
- ✓
$(0, y, z)$
- C
$(0,0, z)$
- D
$(x, y, 0)$
Answer: B.
View full solution →Distance of point $\text {P(a, b, c )}$ from $Z-axis$ is :
- A
$\sqrt{\left(b^2+c^2\right)}$
- B
$\sqrt{\left(a^2+c^2\right)}$
- ✓
$\sqrt{\left(a^2+b^2\right)}$
- D
$\sqrt{\left(a^2+b^2+c^2\right)}$
Answer: C.
View full solution →The distance of point $(1,2,3)$ from $x$-axis is :
- A
$\sqrt{5}$
- B
$\sqrt{10}$
- ✓
$\sqrt{13}$
- D
$1$
Answer: C.
View full solution →The locus of a point is $x-axis$ for which $y=0, z=0$.
View full solution →The perpendicular of point $\text {P(6,7,8)}$ from XY - plane is 8 unit.
View full solution →Points $(a, b, c),(b, c, a)$ and $(c, a, b)$ are vertices of equilateral triangle.
View full solution →The distance of point $\text {P (3,3,4)}$ from $x$-axis is $3$ unit.
View full solution →The distance between points $\text {P(-2,3,1)}$ and $\text {Q (2,1,2)}$ is 21 unit.
View full solution →The coordinates of a point on $y-axis$ be __________ which are at a distance of $\sqrt{10}$ unit from point $(1,2,3).$
View full solution →The distance of point $P (3,4,5)$ from $z-axis $ is __________.
View full solution →The distance of point $P (2,3,5)$ from plane XY is __________.
View full solution →The points $A (4,-3,-1), B (5,-7,6)$ and $C (3,1,-8)$ are __________.
View full solution →The distance between points $P (-2,4,1)$ and $Q (1,2,-5$) is __________.
View full solution →Fill in the blanks :
(i) Plane formed by $x$-axis and $y$-axis is _________.
(ii) Coordinates of a point in XY-plane can be shown as _________.
(iii) Coordinate axes divide the space in __________ octants.
View full solution →Find the distance of point $P(\alpha, \beta, \gamma)$ from coordinate axes.
View full solution →Write the distances of point ( $x, y, z$ ) from three coordinate planes.
View full solution →If distance between points $P (x,-8,4)$ and $Q(-3,-5,4)$ is 5 unit, then find the value of $x$.
View full solution →In which octants are following points lie?
$(\text {i})$ $(3,-1,2)$$\quad$ $(\text {ii})$ $(3,1,2)$
View full solution →If $A(-2,2,3)$ and $B(13,-3,13)$ are two points respectively. A point P moves in such a way that $3 PA =2 PB$. Prove that locus of point P is $x^2+y^2$ $+z^2+28 x-12 y+10 z-247=0$.
View full solution →Show that point $A (1,2,3), B =(-1,-2,-1),$ $C(2,3,2)$ and $D(4,7,6)$ are the vertices of a parallelogram.
View full solution →Prove that following points are collinear :
(i) $(4,-3,-1),(5,-7,6),(3,1,-8)$
(ii) $(0,7,-7),(1,4,-5),(-1,10,-9)$
View full solution →Show that the points $A(0,7,10), B(-1,6,6)$ and $C (-4,9,6)$ are the vertices of an isosceles right - angles triangle.
View full solution →Find the perimeter of a triangle whose verticies have the coordinates $A ( 1 0 , - 2 , 8 ), B ( 8 , 0 , 7 )$ and $C (10,2,8).$
View full solution →| Part (A) | Part (B) |
| 1. Distance between points $P(1,2,3)$ and $Q(-1,-1,-1)$ | (a) $x-2 y-z+1=0$ |
| 2. The locus of a point equidistant from points $A (0,2,3)$ and $B (2,-2,1)$ | (b) $\sqrt{29}$ |
| 3. Point on $y$-axis which is equidistant from points $(3, 1, 2)$ and $(5, 5, 2)$ | (c) $(0,0,7)$ |
| 4. Point on the $z$-axis which is at a distance of $\sqrt{21}$ unit from point $(1,2,3)$ | (d) $(0,5,0)$ |