Page 81 - Mathematics Class - XII

Viva-Voce

1. Define scalar or dot product. 

Ans. Scalar product or dot product of two vectors a and is defined as
b

ab. ab cos where is the angle between a and b 0

i when 0, then .ab = ab ab ii when , then a.. =b a b cos 0
2 2

also aa . aa aa a 2 i j . j k . ki . 0

ii . jj . kk . 1
   
2. If a and are perpendicular vectors, then what is the value of ab. ?
b
     
Ans. ab. ab cos ab cos90 . 0
3. What is the dot product of two like vectors?


Ans. If a and are like vectors, then angle between them is 0°,
b
       
ab. ab cos ab cos0 ab .
4. What is the value of ii iji k⋅      ?
⋅
⋅ ,
,

Ans. ii. 1 . 11 ; 0 ;. 00
ik
ij.
ij cos 90
ii cos 0
ik cos 90


 

5. If the vectors 2i 4 j mk  and 4i 2k are orthogonal, what is the value of m?
j
Ans. We know that dot product of two orthogonal vectors is zero.




So, 2i 4 j mk    j 2k 0
. 4i

0 42m m 2
84 2m
MCQs

j ik.(
1. The value of ij k.( ) ) ki j.( ) is
a) 0 b) –1 c) 1 d) 3
→
→
→
→
2. If θ is the angle between two vectors a and b , the a . b > 0 only when

a) 0 b) 0 c) 0 d) 0
2 2
→
→
→
→
→
→
3. If | a × b | = 4 and | a . b | = 2 the | a | | b | will be equal to
2
2
a) 2 b) 6 c) 8 d) 20

4. If ab bc ca then a b c is equal to
→ → →
a) 2 b b) 2 c c) 0 d) 2 a

Answers: 1. c) 1 2. b) 0 3. d) 20 4. c) 0
2
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