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If a point lies on the z-axis, then find its x-coordinate and y-coordinate.

If a point lies on yz-plane then what is its x-coordinate?

In which plane does the point (4, -3, 0) lie?

In which octant does each of the given points lie?

(i) (-4, -1, -6)

(ii) (2, 3, -4)

(iii) (-6, 5, -1)

(iv) (4, -3, -2)

(v) (-1, -6, 5)

(vi) (4, 6, 8)

Find the distance between the points :

(i) A(5, 1, 2) and B(4, 6, -1)

(ii) P(1, -1, 3) and Q(2, 3, -5)

(iii) R(1, -3, 4) and S(4, -2, -3)

(iv) C(9, -12, -8) and the origin

Show that the points A(1, -1, -5), b(3, 1,3) and C(9, 1, -3) are the vertices of an equilateral triangle.

Show that the points A(4, 6, -5), B(0, 2, 3) and C(-4, -4, -1) from the vertices of an isosceles triangle.

Show that the points A(0, 1, 2), B(2, -1, 3) and C(1, -3, 1) are the vertices of an isosceles right-angled triangle.

Show that the points A(1, 1, 1), B(-2, 4, 1), C(1, -5, 5) and D(2, 2, 5) are the vertices of a square.

Show that the points A(1, 2, 3), B(-1, -2, -1), C(2, 3, 2) and D(4, 7, 6) are the vertices of a parallelogram. Show that ABCD is not a rectangle.

Show that the points P(2, 3, 5), Q(-4, 7, -7), R(-2, 1, -10) and S(4, -3, 2) are the vertices of a rectangle.

Show that the points P(1, 3, 4), Q(-1, 6, 10), R(-7, 4, 7) and S(-5, 1, 1) are the vertices of a rhombus.

Show that D(-1, 4, -3) is the circumcentre of triangle ABC with vertices A(3, 2, -5), B(-3. 8, -5) and C(-3, 2, 1).

Show that the following points are collinear :

A(-2, 3, 5), B(1, 2, 3) and C(7, 0, -1)

A(3, -5, 1), B(-1, 0, 8) and C(7, -10, -6)

P(3, -2, 4), Q(1, 1, 1) and R(-1, 4, 2)

Find the equation of the curve formed by the set of all points which are equidistant from the points A(-1, 2, 3) and B(3, 2, 1).

Find the point on the y-axis which is equidistant from the points A(3, 1, 2) and B(5, 5, 2).

Find the point on the z-axis which is equidistant from the points A(1, 5, 7) and B(5, 1, -4).

Find the coordinates of the point which is equidistant from the points A(a, 0, 0), B(0, b, 0), C(0, 0, c) and O(0, 0, 0).

Find the point in yz-plane which is equidistant from the points A(3, 2, -1), B(1, -1, 0) and C(2, 1, 2).

Find the point in xy-plane which is equidistant from the points A(2, 0, 3), B(0, 3, 2) and C(0, 0, 1).

Find the coordinates of the point which divides the join of A(3, 2, 5) and B(-4, 2, -2) in the ratio 4 : 3.

Let A(2, 1, -3) and B(5, -8, 3) be two given points. Find the coordinates of the point of trisection of the segment AB.

Find the coordinates of the point that divides the join of A(-2, 4, 7) and B(3, -5, 8) extremally in the ratio 2 : 1.

Find the ratio in which the point R(5, 4, -6) divides the join of P(3, 2, -4) and Q(9, 8, -10).

Find the ratio in which the point C(5, 9, -14) divides the join of A(2, -3, 4) and B(3, 1, -2).

Find the ratio in which the line segment having the end points A(-1, -3, 4) and B(4, 2, -1) is divided by the xz-plane. Also, find the coordinates of the point of division.

Find the coordinates of the point where the line joining A(3, 4, 1) and B(5, 1, 6) crosses the xy-plane.

Find the ratio in which the plane x – 2y + 3z = 5 divides the join of A(3, -5, 4) and B(2, 3, -7). Find the coordinates of the point of intersection of the line and the plane.

The vertices of a triangle ABC are A(3, 2, 0), B(5, 3, 2) and C(-9, 6, -3). The bisector AD of ∠ A meets BC at D, find the fourth vertex D.

If the three consecutive vertices of a parallelogram be A(3, 4, -3), B(7, 10, -3) and C(5, -2, 7), find the fourth vertex D.

Two vertices of a triangle ABC are A(2, -4, 3) and B(3, -1, -2), and its centroid is (1, 0, 3). Find its third vertex C.

If the origin is the centroid of triangle ABC with vertices A(a, 1, 3), B(-2, b, -5) and C(4, 7, c), find the values of a, b, c.

The midpoints of the sides of a triangle are (1, 5, -1), (0, 4, -2) and (2, 3, 4). Find its vertices.