RD Sharma

Solutions

Class 12 Maths

Chapter 24Ex 24.1

Scalar or Dot Product Ex 24.1 Q1

Scalar or Dot Product Ex 24.1 Q2

Scalar or Dot Product Ex 24.1 Q3

Scalar or Dot Product Ex 24.1 Q5(ii)

Scalar or Dot Product Ex 24.1 Q5(iii)

Scalar or Dot Product Ex 24.1 Q5(iv)

Scalar or Dot Product Ex 24.1 Q5(v)

Scalar or Dot Product Ex 24.1 Q6

Scalar or Dot Product Ex 24.1 Q7(i)

Scalar or Dot Product Ex 24.1 Q8(i)

Scalar or Dot Product Ex 24.1 Q8(ii)

Scalar or Dot Product Ex 24.1 Q9

Scalar or Dot Product Ex 24.1 Q10

Scalar or Dot Product Ex 24.1 Q11

Scalar or Dot Product Ex 24.1 Q12

Scalar or Dot Product Ex 24.1 Q13

Scalar or Dot Product Ex 24.1 Q15

Scalar or Dot Product Ex 24.1 Q16

Scalar or Dot Product Ex 24.1 Q17

Scalar or Dot Product Ex 24.1 Q18

Scalar or Dot Product Ex 24.1 Q19

Scalar or Dot Product Ex 24.1 Q20

Scalar or Dot Product Ex 24.1 Q21

Scalar or Dot Product Ex 24.1 Q22

Scalar or Dot Product Ex 24.1 Q23

Scalar or Dot Product Ex 24.1 Q24

Scalar or Dot Product Ex 24.1 Q25

Scalar or Dot Product Ex 24.1 Q26

Scalar or Dot Product Ex 24.1 Q27

Scalar or Dot Product Ex 24.1 Q28

Scalar or Dot Product Ex 24.1 Q29

Scalar or Dot Product Ex 24.1 Q30(i)

Scalar or Dot Product Ex 24.1 Q30(ii)

Scalar or Dot Product Ex 24.1 Q31(i)

Scalar or Dot Product Ex 24.1 Q31(ii)

Scalar or Dot Product Ex 24.1 Q31(iii)

Scalar or Dot Product Ex 24.1 Q32(i)

Scalar or Dot Product Ex 24.1 Q32(ii)

Scalar or Dot Product Ex 24.1 Q32(iii)

Scalar or Dot Product Ex 24.1 Q33(i)

Scalar or Dot Product Ex 24.1 Q33(ii)

Scalar or Dot Product Ex 24.1 Q34

Scalar or Dot Product Ex 24.1 Q35

Scalar or Dot Product Ex 24.1 Q36

Scalar or Dot Product Ex 24.1 Q37

Scalar or Dot Product Ex 24.1 Q38

Scalar or Dot Product Ex 24.1 Q39

Scalar or Dot Product Ex 24.1 Q40

Scalar or Dot Product Ex 24.1 Q41

Scalar or Dot Product Ex 24.1 Q42

Scalar or Dot Product Ex 24.1 Q43

Scalar or Dot Product Ex 24.1 Q44

Scalar or Dot Product Ex 24.1 Q45

Scalar or Dot Product Ex 24.1 Q46

Scalar or Dot Product Ex 24.1 Q47

Scalar or Dot Product Ex 24.1 Q48

Scalar or Dot Product Ex 24.1 Q49

la+ 612

= 1612

�<a+ 6).(a + 6> = 6 .5

�a.a+ a.6 + 5.a + 6.6 = 5.6

�a.a+ a.6 + a.6 + 6.6 = 5.6

� a.a+2a.6 =o

� a.(a + 2 5) = o

.·.a+ 26 is perpendicularto a.

Let (a + E) . (a - E) = 0

lal2

-IEl2 = o

1�12

= 1i;i2

lal = IEI

Let Fl= �I Squaring both the sides.

Thus,

lal2

= IEl2

lal2

- IEl2

= o(aJ

2

-(EJ2

= o (a+E) . (a-5) = o

(a+E).(a -5) = o o Fl= fl