Home
Class 11
PHYSICS
If vector (hata+ 2hatb) is perpendicular...

If vector `(hata+ 2hatb)` is perpendicular to vector `(5hata-4hatb)`, then find the angle between `hata and hatb`.

Text Solution

Verified by Experts

The correct Answer is:
`60^(@)`
`because (hata+ 2hatb) `is perpendicular to`(5hata-4hatb)`
`therefore (hata+ 2hatb) *( 5hata - 4hatb) =0`
`rArr 5hata*hata- 4hata*hatb+ 10 hatb*hata- 8hatb*hatb=0`
`rArr 5+ 6hata*hatb-8=0`
`rArr 6hata* hatb=3`
`rArr hata*hatb= (1)/(2)`
`rArr cos theta = (1)/(2)`
`rArr theta = 60^(@)`
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHEMATICS USED IN PHYSICS &VECTORS

    ALLEN|Exercise BEGINNER S BOX 12|4 Videos

  • BASIC MATHEMATICS USED IN PHYSICS &VECTORS

    ALLEN|Exercise TRIGONOMETRY|7 Videos

  • BASIC MATHEMATICS USED IN PHYSICS &VECTORS

    ALLEN|Exercise BEGINNER S BOX 10|3 Videos

  • CENTRE OF MASS

    ALLEN|Exercise EXERCISE-V B|19 Videos

Similar Questions

Explore conceptually related problems

If |hata+hatb|=|hata-hatb| , then find the angle between veca and vecb

Let hata and hatb be two unit vectors. If the vectors vecc=hata+2hatb and vecd=5hata-4hatb are perpendicular to each other then the angle between hata and hatb is (A) pi/2 (B) pi/3 (C) pi/4 (D) pi/6

if veca,vecb and vecc are mutally perpendicular vectors of equal magnitudes, then find the angle between vectors and veca+ vecb+vecc .

Unit vector hata and hatb are perpendicular to each other and the unit vector hatc is inclined at an angle theta to both hata and hatb If hatc=m(hata+hatb)+hatn(hata times hatb) . And m,n are real prove that pi/4 le theta le (3pi)/4 .