Home
Class 12
MATHS
If theta is the angle between the unit v...

If `theta` is the angle between the unit vectors `veca and vecb`, then prove that
`cos((theta)/2)=1/2|veca+vecb|`

Text Solution

Verified by Experts

i. `(veca+vecb).(veca+vecb)= |veca|^(2)+|vecb|^(2)+2veca.vecb`
`=1 +1+2(1)(1) cos theta`
`cos(theta/2)=1/2|veca+vecb|`
ii. `(veca-vecb).(veca-vecb)=|veca|^(2)=|vecb|^(2)-2veca.vecb`
`= 1+1-2(1)(1)cos theta`
`=2-2costheta`
`or sin"theta/2=1/2|veca+vecb|`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.1|18 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.2|15 Videos

  • DETERMINANTS

    CENGAGE PUBLICATION|Exercise All Questions|262 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

Similar Questions

Explore conceptually related problems

If theta is the angle between the unit vectors veca and vecb , then prove that sin (theta/2)=1/2|veca-vecb|

If the angle between unit vectors veca and vecb is 120^(@) . Then find the value of |veca +vecb| .

If theta is the angle between any two vectors vecaandvecb , then |veca*vecb|=|vecaxxvecb| when theta is equal to

Let veca,vecb and vecc be the non zero vectors such that (vecaxxvecb)xxvecc=1/3 |vecb||vecc|veca. if theta is the acute angle between the vectors vecb and vecc then sintheta equals (A) 1/3 (B) sqrt(2)/3 (C) 2/3 (D) 2sqrt(2)/3

If veca,vecb are unit vectors and theta be the angle between them show tat sin((theta)/(2)) = 1/2 |veca-vecb|

What is the angle between vector vecA and the resultant of (vecA+vecB) and (vecA-vecB) ?

If vectors veca and vecb are non collinear then veca/(|veca|)+vecb/(|vecb|) is

The angle between (vecA + vecB) and (vecA xx vecB) is given by—

If veca+vecb=vecc and a+b=c , find the angle between veca and vecb .