Home
Class 12
MATHS
Let vec(alpha)=ai+bj+ck and vec(beta)=b...

Let `vec(alpha)=ai+bj+ck` and `vec(beta)=bi+cj+ak`, where `a`, `b`, `c` `in R` If `theta` be the angle between `alpha` and `beta` then,

Text Solution

Verified by Experts

`vecalpha=ahati+bhatj+chatk`
`vecbeta=bhati+chatj+ahatk`
`vecalpha*vecbeta=ab+bc+ca`
`|vecalpha||vecbeta|costheta=ab+bc+ca`
`costheta=(ab+bc+ca)/(a^2+b^2+c^2)`
`1/2((a+b+c)^2-(a^2+b^2+c^2))/(a^2+b^2+c^2)`
`costheta> -1/2`
`theta in (pi-pi/3,pi)`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Given that (vec beta-vec alpha) * (vec beta + vec alpha) = 8 and vec alpha * vec beta = 2 Also | vec alpha | = 1 then angle between (vec beta-vec alpha) and (vec beta + vec alpha) is

If |vec alpha + vec beta |=| vec alpha - vec beta|, then :

Let vec alpha=2i+3j-k and vec beta=i+j. If vec gamma is a unit vector,then the maximum value of [vec alpha xxvec beta,vec beta xxvec gamma,vec gamma xxvec alpha] is equal to

If vec(a) = hat(i) + 2 hat(j) - 3 hat (k) and vec(beta) = 3 hat(i) - hat (j) + 2 hat (k) , find the cosine of the angle between the vectors (2 vec(alpha)+ vec(beta)) and (vec(alpha)+2 vec(beta))

If alpha, beta are solutions of a cos theta + b sin theta = c where a, b, c in R and a^(2) + b^(2) gt 0, cos alpha ne cos beta, sin alpha ne sin beta then prove that sin alpha sin beta = (c^(2)-a^(2))/(a^(2) + b^(2))

If alpha, beta are solutions of a cos theta + b sin theta = c where a, b, c in R and a^(2) + b^(2) gt 0, cos alpha ne cos beta, sin alpha ne sin beta then prove that sin alpha + sin beta = (2bc)/(a^(2) + b^(2))

If alpha and beta are two nonzero and different vectors such that |vec alpha + vec beta| = |vec beta - vec alpha| then the angle between the vectors vec alpha and vec beta is