6quad " If "|vec a|=2," find "|vec a times i|^(2)+|vec a timeshat j|^(2)+|vec a timeshat k|^(2)

If |vec a|=2, then find the value of |vec a xxhat i|^(2)+|vec a xxhat j|^(2)+|vec a xxhat k|^(2)

For any vector vec(a), |vec(a)xx hat(i)|^(2)+ |vec(a)xx hat(j)|^(2)+ |vec(a) xx hat(k)|^(2) is equal to

If vec a = i-j+k and vec b = 2i+j-k then |2 vec a - vec b|=

For any vector vec a , the value of (vec a xx i)^(2) + (vec a xx j)^(2) + (vec a xx k)^(2) =

If vec a = hat i - hat j and vec b = hat j + hat k then |vec a xx vec b|^(2) + |vec a. vecb|^(2) is equal to

Assertion (A): Let vec(a) = a_(1) vec(i) + a_(2) vec(j) + a_(3) vec(k) . Then identity |vec(a) xx vec(i)|^(2) + |vec(a) xx vec(j)|^(2) + |vec(a) xx vec(k)|^(2) =2|vec(a)|^(2) holds for vec(a) . Reason (R ): vec(a) xx vec(i) = a_(3) vec(j)- a_(2) vec(k), vec(a) xx vec(j) = a_(1) vec(k) - a_(3) vec(i), vec(a) xx vec(k)= a_(2) vec(i) - a_(1) vec(j) Which of the following is correct ?

If vec a= i- j and vec b=- j+2k ,find (vec a-2 vec b)dot( vec a+ vec b)

If vec a xx i+2vec a-4vec i-2vec j+vec k=0 then vec a=

If vec a = 2vec i + 2vec j + vec kvec b = 5vec i + vec j + 2vec k then | vec a xxvec b | ^ (2) + (vec a * vec b) ^ (2) =