Daily Practice Problems

Class 11 Maths

Introduction to Three Dimensional Geometry

Class 11 Maths

Introduction to Three Dimensional Geometry

**Question 1:**

Locate the following points in the space.

(i) (1, -1, 3) (ii) (-1, 2, 4)

(iii) (-2, -4, -7) (iv) (-4, 2, -5)

**Question 2:**

How far apart are the points (2, 0, 0) and (-3, 0, 0)?

**Question 3:**

Find the third vertex of triangle whose centroid is origin and two vertices are (2,4,6) and (0, -2, -5).

**Question 4:**

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.

**Question 5:**

The distance of point P(3, 4, 5) from the yz-plane is

(a) 3 units

(b) 4 units

(c) 5 units

(d) 550 units

**Question 6:**

If the distance between the points (a, 0, 1) and (0, 1, 2) is √27, then what is the value of a?

**Question 7:**

Three consecutive vertices of a parallelogram ABCD are A(6, -2, 4), B(2, 4, -8) and C(-2, 2, 4). Find the coordinates of the fourth vertex.

**Question 8:**

Show that the triangle ABC with vertices A(0, 4, 1), B(2, 3, -1) and C(4, 5, 0) is right angled.

**Question 9:**

Find the equation of the set of points which are equidistant from the points

(1, 2, 3) and (3, 2, –1).

**Question 10:**

Find the co ordinate of the point which divides the join of P(2, -1, 4) and Q(4, 3, 2) in the ratio 2 : 5 (i) internally (ii) externally.

**Question 11:**

x = a represents a plane parallel to ____.

**Question 12:**

The equation of z-axis, are ______.

**Question 13:**

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

**Question 14:**

What are the coordinates of the vertices of a cube whose edge is 2 units, one of whose vertices coincides with the origin and the three edges passing through the origin, coincides with the positive direction of the axes through the origin?

**Question 15:**

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

**Question 16:**

Show that, if x^{2} + y^{2} = 1, then the point {x, y, √(1 - x^{2} - y^{2})} is at a distance unit from the origin.

**Question 17:**

Let A, B, C be the feet of perpendiculars from a point P on x, y, z-axis respectively. Find the coordinates of A, B and C in each of the following where the P is (i) (3, 4, 2) (ii) (– 5, 3, 7) (iii) (4, – 3, – 5)

**Question 18:**

If a parallelepiped 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 parallelepiped is __________.

**Question 19:**

The length of the longest piece of a string that can be stretched straight in a rectangular room whose dimensions are 10, 13 and 8 units are _____.

**Question 20:**

The locus of a point for which y = 0, z = 0 is

(a) equation of x-axis

(b) equation of y-axis

(c) equation of z-axis

(d) None of these

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