Page 78 - Mathematics Class - XII

Viva-Voce

1. Explain cross product of two vectors.
 
b
n
Ans. The cross or vector product of two non-zero vectors a and b , is a ab sin
   

Where q is the angle between a and b , 0 ≤ θ ≤ π. Also, n is a unit vector perpendicular to both a and b


such that ab, and n form a right-handed system.
2. Define scalar product of two vectors.   
Ans. The scalar or dot product of two non-zero vectors a and b , denoted by ab.
   
So, ab . ab cos , where q is the angle between a and b and 0 ≤ q ≤ π

 
3. What is the value of i j  jk  ?

i
j k
i
j
jk
Ans. i j So, j
ki
k and

4. Find the unit vector in the direction of the sum of the vectors, a =2i 2 j 5k and b 2i 1j 3k

Ans. a =2i 2 j 5k and b 2i 1j 3k
ab 22 i 21 j 33 i 3 j 2k

k

4
5

Let c a b 4 i 3 j 2k
2
2
2 2
Magnitudeof c 4 3 2 16 94 29

c

Unit vector, n 1 4 j 2k
3
i
c 29
MCQs
     j then the value of λ will be

j k
1. If vector 2i is perpendicular to the vector i 4 k,
a) 0 b) –1 c) –2 d) –3
→
→
→
→
2. If the angle between the vectors a and b is θ, then the angle between the vectors 2 a and 3 b is
q q q
a) b) c) θ d)
3 2 4
→
→
→
→
3. If the angle between the two vectors a and b is θ, then a . b > θ when only
a) 0 b) 0 c) 0 < θ < π d) 0 < θ < π
2 2
→
→
→
→
4. Let a and b both are unit vectors and θ is the angle between them, then a + b is the unit vector if

a) b) c) d)
4 3 2 3
→
→
→
→
5. If two unit vectors a and b are in such a way that the angle between them is 60°, then the value of | a – b | is
a) 5 b) 3 c) 2 d) 1

Answers: 1. b) –1 2. c) θ 3. b) 0 4. d) 5. d) 1
2 3
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