Home
Class 11
PHYSICS
IF veca=2veci+3vecj+4veck and vecb =3vec...

IF `veca=2veci+3vecj+4veck and vecb =3veci+4vecj+5veck` find the angle between `veca and vecb`.

Text Solution

Verified by Experts

We have `veca.vecb=ab costheta`
or `costheta= (veca.vecb)/(ab)`
where `theta` is the angle between `veca and vecb`
Now `veca.veb=a_xb_x+a_yb_y+a_zb^z`
`=2xx4+3xx3+4xx2=25`
Also, `veca=sqrt(a_x^2+a_y^2+a_z^2)
`=sqrt(4+9+16)= sqrt29`
and ` b= sqrt(b_x^2+b_u^2+b_z^2= sqrt(16+9+4)= sqrt(16+9+4)=sqrt29`
Thrus, `costheta = 25/29`
`or, `theta= cos^-1 (25/29)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

If vecA xx vecB= vec0 and vecB xx vecC=vec0 , then the angle between vecA and vecC may be :

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

If veca+vecb+vecc=vec0, |veca| = 3, |vecb| = 5, |vecc| = 7 , then angle between veca and vecb is

if| vecAxxvecB|=|vecA.vecB| , then angle between vecA and vecB will be

If vecA.vecB=vec0 and vecAxxvecC=vec0 , then the angle between vecB and vecC is

If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4vecb are perpendicular to each other, then the angle between veca and vecb is

If vecA+ vecB = vecC and A+B=C , then the angle between vecA and vecB is :

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

If vecA*vecB=AB , then angle between vecA and vecB will be …... .

If vecA+ vecB = vecC and A+B+C=0 , then the angle between vecA and vecB is :