Intermediate Maths Solutions for Exercise 4(a) Addition of Vectors (class 11 maths)
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.
You can 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 (class 11 maths)
Class 11 math solution (Inter)
Addition of Vectors – Exercise 4(a)
Questions and solutions
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.
