# Intermediate Maths Solutions for Exercise 4(a) Addition of Vectors

Intermediate mathematics IA Exercise 4(a) Addition of Vectors textbook solutions are given.

These solutions are very easy to understand.

You should study the textbook lesson Addition of Vectors very well.

Then you should also observe the example problems and solutions given in the text book. Try them.

Observe the solutions given below. Try them in your own method.

**You can also see**

Inter Maths 1A textbook solutions

Inter Maths 1B textbook solutions

Inter Maths IIA textbook solutions

Inter Maths IIB textbook solutions

**Addition of vectors textbook solutions**

SSC Maths text book Solutions class 10

Model papers for maths SSC class 10 and Inter

## Inter Maths solutions for Exercise 4(a) Addition of Vectors

**Addition of Vectors – Exercise 4(a)**

Problem

In ∆ABC, P, Q and R are the midpoints of the sides AB, BC and CA respectively. If D is any point,

then express DA + DB + DC in terms of DP, DQ and DR.

If PA + QB + RC = alfa then find alfa.

Problem

Let a = i + 2j + 3k and b = 3i + j. Find the unit vector in the direction of a + b.

Problem

If OA = i + j + k and AB = 3i – 2j + k, BC = i + 2j – 2k and CD = 2i + j + 3k, then find the vector OD

Problem

a = 2i + 5j + k and b = 4i + mj + nk are collinear vectors, then find m and n.

Problem

Let a = 2i + 4j – 5k, b = i + j + k and c = j + 2k. Find the unit vector in the opposite direction a + b + c.

Problem

Is the triangle formed by the vectors 3i + 5j – 2k, 2i – 3j – 5k and – 5i – 2j + 3k equilateral ?

Problem

Find the angles made by the straight line passing through the points (1, – 3, 2) and (3, – 5, 1) with the coordinates axes.

## Maths Solutions for Addition of Vectors Exercise 4(a)

Problem

Problem

a, b, c are non-coplanar vectors. Prove that the following four points are coplanar.

-a + 4b – 3c,. 3a + 2b – 5c,. – 3a + 8b – 5c,. – 3a + 2b + c.

Problem

6a + 2b – c,. 2a – b + 3c,. – a + 2b – 4c,. – 12a – b – 3c.

If i, j, k are unit vectors along the positive directions of the coordinate axes, then show that the four points 4i + 5j + k, – j – k, 3i + 9j + 4k and – 4i + 4j + 4k are coplanar.

Problem

If a, b, c are non-coplanar vectors, then test for the collinearity of the following points whose position vectors are given by

a – 2b + 3c,. 2a + 3b – 4c,. -7b – 10c.

Problem

3a – 4b + 3c,. – 4a + 5b – 6c,. 4a – 7b + 6c.

Problem

2a + 5b – 4c,. a + 4b – 3c,. 4a + 7b – 6c.

## Addition of Vectors Exercise 4(a) Solutions Inter

Problem

In the Cartesian plane, O is the origin of the coordinate axes, A is a person starts at O and walks a distance of 3 units in the NORTH – EAST direction and reaches the point P, From P he walks 4 units of distance parallel to NORTH – WEST direction and reaches the point Q. Express the vector OQ in terms of i and j (observe that angle XOP = 45°).

Problem

The points O, A, B, X and Y are such that OA = a, OB = b, OX = 3a and OY = 3b. Find BX and AY in terms of a and b. Further, if the points P divide AY in the ratio 1 : 3, then express BP interms of a and b

Problem

In ∆OAB, E is the midpoint of AB and F is a point on OA such that OF = 2FA. If C is the point of intersection of OE and BF, then find the ratios of OC : CF and BC : CF.

Problem

The point E divides the segment PQ internally in the ratio 1 : 2 and R is any point not on the line PQ. If F is a point on QR such that QF : FR = 2 : 1, then show that EF is parallel to PR.

**Note** : Observe the solutions and try them in your own method.

**Some more**

Problem

Let ABCDEF be a regular hexagon with centre ‘O’ show that AB + AC + AD + AE + AF =3 AD = 6 AO.