NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra — Exercise 10.3

Question 1:Find the angle between two vectors a b and with magnitudes 3 and 2 , respectively having a b 6 .

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Question 2:Find the angle between the vectors ˆ ˆ ˆ i jk 2 3 and ˆ ˆ ˆ 3 2 i jk

Question 3:Find the projection of the vector ˆ ˆ i j on the vector ˆ ˆ i j .

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Question 4:Find the projection of the vector ˆ ˆ ˆ i jk 3 7 on the vector ˆ ˆ ˆ 7 8 ij k .

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Question 5:Show that each of the given three vectors is a unit vector: 11 1 ˆˆ ˆˆ ˆˆ ˆˆ ˆ (2 3 6 ), (3 6 2 ), (6 2 3 ) 77 7 i jk i jk i jk ✓ ✓ Also, show that they are mutually perpendicular to each other

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Question 6:Find | | and | | a b , if ( )( ) 8 ab ab a b and | |8 | | .

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Question 7:Evaluate the product (3 5 ) (2 7 ) ab ab .

Question 8:Find the magnitude of two vectors a b and , having the same magnitude and such that the angle between them is 60o and their scalar product is 1 2 .

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Question 9:Find | | x , if for a unit vector a , ( )( ) 1 xa xa 2 .

Question 10:If ˆ ˆ ˆ ˆ ˆˆ ˆ ˆ a i j kb i jk c i j 2 2 3 , 2 and 3 are such that a b is perpendicular to c , then find the value of .

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Question 11:Show that || || ab ba is perpendicular to || || ab ba , for any two nonzero vectors a b and .

Question 12:If aa ab 0 and 0 , then what can be concluded about the vector b ?

1. Find the angle between two vectors a b and

Question 13:If abc , , are unit vectors such that abc 0 , find the value of ab bc ca .

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Question 14:If either vector ab a 0 or 0, then 0 b . But the converse need not be true. Justify your answer with an example.

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Question 15:If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ✓ABC. [✓ABC is the angle between the vectors BA ✔✔✔✕ and BC ✖✖✖ ].

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Question 16:Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, –1) are collinear.

Question 17:Show that the vectors ˆˆ ˆ ˆ ˆ ˆ ˆˆ ˆ 2 ,3 i j ki j k i j k 5 and 3 4 4 form the vertices of a right angled triangle.

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Question 18:If a is a nonzero vector of magnitude ‘a’ and a nonzero scalar, then a is unit vector if (A) = 1 (B) = – 1 (C) a = | | (D) a = 1/| |