NCERT Solutions Class 12 Maths Chapter 10 - Vector Algebra

Q1: Find the angle between two vectors   and vector  with magnitudes √3  and 2, respectively having
Ans:


Q2: Find the angle between the vectors
Ans: The given vectors are .



Q3: Find the projection of the vector  on the vector .


Q4: Find the projection of the vector   on the vector  .


Question 5: Show that each of the given three vectors is a unit vector




Q6:  Find , if
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Q7: Evaluate the product 
Ans: 


Q8: Find the magnitude of two vectors a and b, having the same magnitude and such that the angle between them is 60° and their scalar product is 1/2.


Q9: Find , if for a unit
Ans:


Q10: Show that   is perpendicular to    ,for any two nonzero vectors a and b.
Ans: 


Q11: If , then what can be concluded about the vector ?


Q12: If  are unit vectors such that , find the value of  
Ans:


Q13: If either vector a = 0, then b = 0. But the converse need not be true. Justify your answer with an example.
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Q14:

Ans: The vertices of ΔABC are given as A (1, 2, 3), B (–1, 0, 0), and C (0, 1, 2).


Q15: Show that the points A (1, 2, 7), B (2, 6, 3) and C (3, 10, –1) are collinear.
Ans: The given points are A (1, 2, 7), B (2, 6, 3), and C (3, 10, –1).


Q16: Show that the vectors 2i - j k, i - 3j - 5k and 3i - 4j - 4k  form the vertices of a right angled triangle.


Q17:  nonzero vector of magnitude ‘a’ and λ a nonzero scalar, then  is unit vector if
(A) λ = 1
(B) λ = –1    
(c) a = | λ|
(d) a = 1/| λ|
Ans:  Vector  is a unit vector if