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 
Ans:
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.
Ans:
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 
