Q. A point is on the $x$-axis. What are its $y$-coordinate and $z$-coordinates?

Q. If a point is in the $XZ$-plane. What can you say about its $y$-coordinate?

Q. Fill in the blanks:
(i) The $x$-axis and $y$-axis taken together determine a plane known as______
(ii) The coordinates of points in the $XY$-plane are of the form_____
(iii) Coordinate planes divide the space into_____ octants

Q. Name the octants in which the following points lie:
$(1,2,3),(4,-2,3)(4,-2,-5),(4,2,-5),(-4,2,-5),(-4,2,5),(-3,-1,6),(2,-4,-7)$

Q. Verify the following
(i) $(0,7,-10),(1,6,-6)$ and $(4,9,-6)$ are the vertices of an isosceles triangle
(ii) $(0,7,10),(-1,6,6)$ and $(-4,9,6)$ are the vertices of a right angled triangle
(iii) $(-1,2,1),(1,-2,5),(4,-7,8)$ and $(2,-3,4)$ are the vertices of a parallelogram

Q. Find the equation of the set of points $P$, the sum of whose distances from $A(4,0,0)$ and $B(-4,0,0)$ is equal to $10$.

Q. Find the distance between the following pairs of points:
(i) $(2,3,5)$ and $(4,3,1)$
(ii)$(-3,7,2)$and $\left(\right(2,4,-1)$
(iii) $(-1,3,-4)$ and $(1,-3,4)$
(iv) $(2,-1,3)$ and $(-2,1,3)$

Q. Find the equation of the set of points which are equidistant from the points $(1,2,3)$ and $(3,2,-1)$

Q. Show that the points $(-2,3,5),(1,2,3)$ and $(7,0,-1)$ are collinear.

Q. Using section formula show that the points $A(2,-3,4),B(-1,2,1)$ and $C(0,\frac{1}{3},2)$ are collinear.

Q. Find the ratio in which the $YZ$-plane divides the line segment formed by joining the points $(-2,4,7)$ and $(3,-5,8)$

Q. Find the coordinates of the points which trisect the line segment joining the points $P(4,2,-6)$ and $Q(10,-16,6)$

Q. Find the coordinates of the point which divides the line segment joining the points $(-2,3,5)$ and $(1,-4,6)$ in the ratio
(i) $2:3$ internally
(ii) $2:3$ externally

Q. Given that $P(3,2,-4),Q(5,4,-6)$ and $R(9,8,-10)$ are collinear. Find the ratio in which $Q$ divides $PR$.

Q. Find the lengths of the medians of the triangle with vertices $A(0,0,6),B(0,4,0)$ and $(6,0,0).$

Q. A point $R$ with $x$-coordinate $4$ lies on the line segment joining the points $P(2,-3,4)$ and $Q(8,0,10)$. Find the coordinates of the point $R$.

Q. Three vertices of a parallelogram $ABCD$ are $A(3,-1,2),B(1,2,-4)$ and $C(-1,1,2)$. Find the coordinates of the fourth vertex.

Q. If the origin is the centroid of the triangle $PQR$ with vertices $P(2a,2,6),Q(-4,3b,-10)$ and $R(8,14,2c),$ then find the values of $a,b$ and $c$

Q. Find the coordinates of a point on $y$-axis which are at a distance of $5\sqrt{2}$ from the point $P(3,-2,5)$

Q. If $A$ and $B$ be the points $(3,4,5)$ and $(-1,3,-7)$ respectively. Find the equation of the set of points $P$ such that $P{A}^2$ +$P{B}^2$ $=K{}^2$, where $K$ is a constant