Home
Class 12
PHYSICS
Given |vec(A)(1)|=2,|vec(A)(2)|=3 and |v...

Given `|vec(A)_(1)|=2,|vec(A)_(2)|=3` and `|vec(A)_(1)+vec(A)_(2)|=3`. Find the value of `(vec(A)_(1)+2vec(A)_(2)).(3vec(A)_(1)-4vec(A)_(2))`.

Text Solution

Verified by Experts

` | vecA _ 1 + vecA _ 2 | ^ 2 = | vec A _ 1 | ^ 2 + |vecA _ 2 | ^ 2 + 2 | vecA _ 1 | | vecA _ 2 | cos theta `
` 25 = 9 + 25 + 2 xx 15 cos theta `
` rArr cos theta = ( -3 ) / (10 ) `
` rArr vecA _ 1 . vecA _ 2 = | vecA _1 || vecA _ 2 | cos theta = 3 xx 5 xx ( ( -3 ) /(10)) = ( -9 ) /(2 ) `
` ( 2 vecA _ 1 + 3 vecA _ 2 ) . ( 3 vecA _ 1 - 2 vecA _ 2 ) = 6 | vecA _ 1 | ^ 2 - 3 | vecA _ 2 | ^ 2 + 5 vecA _ 1 . vecA _ 2 `
`= 54 - 150 + 5 (( - 9 ) /(2)) = - 118.5 `
Promotional Banner

Topper's Solved these Questions

  • JEE Main Revision Test-9 | JEE-2020

    VMC MODULES ENGLISH|Exercise PHYSICS SECTION 2|5 Videos

  • JEE Main Revision Test-6 | JEE-2020

    VMC MODULES ENGLISH|Exercise PHYSICS|2 Videos

  • JEE MAIN REVISON TEST-23

    VMC MODULES ENGLISH|Exercise PHYSICS (SECTION 2)|1 Videos

Similar Questions

Explore conceptually related problems

|vec(a)|=2, |vec(b)|=3 and vec(a).vec(b)= -8 , then the value of |vec(a) + 3vec(b)| is

If vec(v)_(1)+vec(v)_(2) is perpendicular to vec(v)_(1)-vec(v)_(2) , then

If vec(a_(1)) and vec(a_(2)) are two non-collinear unit vectors and if |vec(a_(1)) + vec(a_(2))|=sqrt(3) , then the value of (vec(a_(1))-vec(a_(2))). (2 vec(a_(1))+vec(a_(2))) is :

If |vec(A)| = 4N, |vec(B)| = 3N the value of |vec(A) xx vec(B)|^(2) + |vec(A).vec(B)|^(2) =

If vec(E)_(1) and vec(E)_(2) are electric field at axial point and equatorial point of an electric dipole, then (1) vec(E)_(1).vec(E)_(2)gt 0 (2) vec(E)_(1).vec(E)_(2)=0 (3) vec(E)_(1).vec(E)_(2)lt 0 (4) vec(E)_(1)+vec(E)_(2)=vec(0)

If | vec a|=2| vec b|=5 and | vec axx vec b|=8, then find the value of vec a . vec bdot

If |vec(a) | = 3, | vec(b) | =4 and | vec(a) xx vec(b) | = 10 , then | vec(a). vec(b) |^(2) is equal to

If vec(a) and vec(b) are two vectors such that |vec(a)|= 2, |vec(b)| = 3 and vec(a)*vec(b)=4 then find the value of |vec(a)-vec(b)|

If |vec(a) xx vec(b)|^(2) + |vec(a) .vec(b)|^(2) = 400 and |vec(a)| = 5 , then write the value of |vec(b)| .

If | vec(a) xx vec(b) | =4 and | vec(a). vec(b) |=2 , then | vec( a) |^(2) | vec( b) | ^(2) is equal to