Home
Class 11
PHYSICS
vec(a) and vec(b) are unit vectors and a...

`vec(a)` and `vec(b)` are unit vectors and angle between them is `pi/k`. If `vec(a)+2vec(b)` and `5vec(a)-4vec(b)` are perpendicular to each other then find the integer value of k.

Text Solution

Verified by Experts

The correct Answer is:
3
`(veca+2vecb).(5veca-4vecb)=0rArr 5a^(2)+10veca.vecb-8vecb^(2)-4veca.vecbrArr -3+6veca.vecb=0`
`rArr ab cos theta=3/6 rArr cos theta=1/2=theta=pi/3rArr k=3`
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS

    ALLEN |Exercise Part -II Example|61 Videos

  • MISCELLANEOUS

    ALLEN |Exercise Part -II Example Some worked out Examples|1 Videos

  • KINEMATICS (MOTION ALONG A STRAIGHT LINE AND MOTION IN A PLANE)

    ALLEN |Exercise BEGINNER S BOX-7|8 Videos

  • PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT

    ALLEN |Exercise EXERCISE-IV|7 Videos

Similar Questions

Explore conceptually related problems

If vec(a)=5hati-hatj+7hatk and vec(b)=hati-hatj+lambda hatk . If vec(a)+vec(b) and vec(a)-vec(b) are perpendicualr to each other then find the value of lambda .

Let vec(a) and vec(b) be two unit vectors and theta is the angle between them. Then vec(a)+vec(b) is a unit vector if ……….

vec(a)=lambda hati+3hatj+2hatk,vec(b)=hati-hatj+3hatk . If vec(a) and vec(b) are perpendicular to each other then find the value of lambda .

Find |vec(a)-vec(b)| , if two vectors vec(a) and vec(b) are such that |vec(a)|=2,|vec(b)|=3 and vec(a).vec(b)=4 .

If |vec(a)|=2,|vec(b)|=5 and vec(a).vec(b)=10 then find |vec(a)-vec(b)| .

If |vec(a)|=2|vec(b)|=5 and |vec(a)xx vec(b)|=8 then find vec(a).vec(b) .

If theta is angle between two vectors vec(a) and vec(b) then vec(a).vec(b)ge 0 only when …….

If |vec(a)|=10,|vec(b)|=2 and vec(a).vec(b)=12 then find |vec(a)xx vec(b)| .

The vector (vec(a)+3vec(b)) is perpendicular to (7 vec(a)-5vec(b)) and (vec(a)-4vec(b)) is perpendicular to (7vec(a)-2vec(b)) . The angle between vec(a) and vec(b) is :

|vec(a)|=3,|vec(b)=(sqrt(2))/(3) . If vec(a)xx vec(b) is a unit vector then find the angle between vec(a) and vec(b) .