Home
Class 11
PHYSICS
Angle between vec(a) and vec(b) is 60^(@...

Angle between `vec(a)` and `vec(b)` is `60^(@)` then

A

The compound of `vec(a)-vec(b)` will be `(a^(2)-b^(2))/sqrt(a^(2)+b^(2)+ab)`

B

`vec(a)xx vec(b)` is perpendicular to resultant of `(vec(a)+2vec(b))` and `(vec(a)- vec(b))`

C

The component of `vec(a)-vec(b)` along `vec(a)+vec(b)` will be `(a^(2)-b^(2))/sqrt(a^(2)+b^(2)+2ab)`

D

The component of `vec(a)+vec(b)` along `vec(a)-vec(b)` will be `(a^(2)-b^(2))/sqrt(a^(2)+b^(2)+sqrt(3)ab)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
For (A) : Required component `=((vec(a)-vec(b)).(vec(a)+vec(b)))/(|vec(a)+vec(b)|)=(a^(2)-b^(2))/sqrt(a^(2)+b^(2)+2ab cos 60^(@))=(a^(2)-b^(2))/sqrt(a^(2)+b^(2)+ab)`
For (B) : `vec(a)+2vec(b)+vec(a)-vec(b)=2vec(a)+vec(b)` which lies in the plane of `vec(a)` and `vec(b)`
`rArr` resultant is perpendicular to `vec(a)xxvec(b)`
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

vec(a)_|_vec(b) and vec(c),|vec(a)|=2,|vec(b)|=3,|vec( c )|=4 . The angle between vec(b) and vec( c ) is (2pi)/(3) then |[vec(a) vec(b) vec( c )]| = …………

Let vec(A), vec(B) and vec(C) , be unit vectors. Suppose that vec(A).vec(B)=vec(A).vec(C)=0 and the angle between vec(B) and vec(C) is pi/6 then

Let vec(a)=2hati+hatj-2hatk and vec(b)=hati+hatj . Let the vector vec( c ) is such that |vec( c )-vec(a)|=3,|(vec(a)xx vec(b))xx vec( c )|=3 . The angle between vec( c ) and vec(a)xx vec(b) is 30^(@) . Then vec(a).vec( c ) = ……………

What is the angle between vec(a) and vec(b) : (i) Magnitude of vec(a) and vec(b) are 3 and 4 respectively. (ii) Area of triangle made by vec(a) and vec(b) is 10.

Given that P=Q=R . If vec(P)+vec(Q)=vec(R) then the angle between vec(P) and vec(R) is theta_(1) . If vec(P)+vec(Q)+vec(R)=vec(0) then the angle between vec(P) and vec(R) is theta_(2) . The relation between theta_(1) and theta_(2) is :-

Let |vec(x)|=|vec(y)|=|vec(x)+vec(y)| =1 and if measure of the angle between vec(x) and vec(y) is alpha , then cos alpha = …………

The centroid of DeltaABC is G. The angle between vec(GB) and vec(GC) is obtuse angle then …………..

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

Let vec(a),vec(b) and vec( c ) be unit vectors such that vec(a).vec(b)=vec(a).vec( c )=0 and the angle between vec(b) and vec( c ) is (pi)/(6) . Prove that vec(a)=+-2(vec(b)xx vec( c )) .

vec(a),vec(b) and vec( c ) are non zero vectors. (vec(a)xx vec(b))xx vec( c )=(1)/(3)|vec(b)||vec( c )|vec(a) . If the acute angle between the vectors vec(b) and vec( c ) is theta then sin theta = ……………