`| veca + vecb |^2 = | veca - vecb |^2`

If for any two vectors veca and vecb. (veca + vecb )^(2) + (veca - vecb)^(2) =lamda[(veca)^(2)+ (vecb)^(2)] then write the value of lamda.

|veca pm vecb|^2 = |veca|^2 + |vecb|^2 pm 2|veca||vecb|cos theta and (veca + vecb).(veca - vecb) = |veca|^2 - |vecb|^2

If |veca xx vecb|^(2) + |veca.vecb|^(2)=144 and |veca|=4 , then find the value of |vecb|

If veca and vecb are non - zero vectors such that |veca + vecb| = |veca - 2vecb| then

vectors veca and vecb are inclined at an angle theta = 60^(@). " If " |veca|=1, |vecb| =2 , " then " [ (veca + 3vecb) xx ( 3 veca -vecb)] ^(2) is equal to

Show that (veca xx vecb)^(2) = |veca| ^(2) |vecb|^(2) - (veca.vecb)^(2) = |(veca.veca)/(veca. vecb)(veca.vecb)/(vecb.vecb)|

The value of the expression |veca xx vecb|^(2) + (veca.vecb)^(2) is-

Prove that | vecaxxvecb | ^ 2 = det ((veca.veca, veca.vecb), (veca.vecb, vecb.vecb))

If veca, vecb, vecc are non-coplanar vectors, prove that the following vectors are coplanar. (i) 3veca - vecb - 4vecc, 3veca - 2vecb + vecc, veca + vecb + 2vecc (ii) 5veca +6vecb + 7vecc, 7veca - 8vecb + 9vecc, 3veca + 20 vecb + 5vecc