NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra — Exercise 10.2

Question 1:Compute the magnitude of the following vectors: 11 1 ˆˆ ˆ ˆ ˆ ˆ ˆ ˆ ; 2 7 3 ; 333 ai jk b i j k c i j k

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Question 2:Write two different vectors having same magnitude.

Question 3:Write two different vectors having same direction.

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Question 4:Find the values of x and y so that the vectors 2 3 and ˆˆ ˆˆ i j xi yj are equal.

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Question 5:Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (– 5, 7).

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Question 6:Find the sum of the vectors ˆˆ ˆˆ ˆ ˆ a i j kb i j k 2 , 245 and ˆ ˆ ˆ ci j k 6 –7 .

Question 7:Find the unit vector in the direction of the vector ˆ ˆ ˆ ai j k 2 .

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Question 8:Find the unit vector in the direction of vector PQ, where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.

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Question 9:For given vectors, ˆˆ ˆˆ ˆ ˆ a i j k b i jk 2 2 and , find the unit vector in the direction of the vector a b .

Question 10:Find a vector in the direction of vector ˆ ˆ ˆ 5 2 ij k which has magnitude 8 units.

Question 11:Show that the vectors ˆˆ ˆˆ ˆ ˆ 2 3 4 and 4 6 8 i jk i jk are collinear.

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Question 12:Find the direction cosines of the vector ˆ ˆ ˆ i jk 2 3 .

1. Compute the magnitude of the following vectors:

Question 13:Find the direction cosines of the vector joining the points A (1, 2, –3) and B(–1, –2, 1), directed from A to B.

Question 14:Show that the vector ˆ ˆ ˆ i jk is equally inclined to the axes OX, OY and OZ.

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Question 15:Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are ˆ ˆ ˆˆ ˆ ˆ i jk i jk 2 and – respectively, in the ratio 2 : 1 (i) internally (ii

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Question 16:Find the position vector of the mid point of the vector joining the points P(2, 3, 4) and Q(4, 1, –2).

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Question 17:Show that the points A, B and C with position vectors, ˆ ˆ ˆ ai jk 3 4 4, ˆ ˆ ˆ b i jk 2 and ˆ ˆ ˆ ci j k 3 5 , respectively form the vertices of a right angled triangle.

Question 18:In triangle ABC (Fig 10.18), which of the following is not true: (A) AB + BC + CA = 0 ✂ ✂ ✂ (B) AB BC AC 0 (C) AB BC CA 0 (D) AB CB CA 0

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Question 19:If a b and are two collinear vectors, then which of the following are incorrect: (A) b a , for some scalar (B) a b (C) the respective components of a b and are proportional (D) both the vectors a b and have same direction, but different magnitu