[" 12.If the vectors "bar(alpha)=ahat i+ahat j+chat k,vec beta=hat i+hat k" and "gamma=chat i+chat j+bk" are coplanar,then prove that "c],[" the geometric mean of "a" and "b.]

If the vectors vec alpha=ahat i+ahat j+chat k,vec beta=hat i+hat k and vec gamma=chat i+chat j+bhat k are coplanar,then prove that c is the geometric mean of a and b.

If the vectors vecalpha=a hat i+a hat j+c hat k , vecbeta= hat i+ hat k and vec gamma=c hat i+c hat j+b hat k are coplanar, then prove that c is the geometric mean of a and b.

If the vectors vecalpha=a hat i+a hat j+c hat k , vecbeta= hat i+ hat k and vec gamma=c hat i+c hat j+b hat k are coplanar, then prove that c is the geometric mean of a and b.

If the vectors ahat(i)+ahat(j)+chat(k),hat(i)+hat(j) andchat(i)+chat(j)+bhat(k) are coplanar, prove that c is the geometric mean of a and b .

If the vector ahat i+ a hat j+ c hatk, hat i+hatk and chat i+c hat j+b hat k be coplanar, show that c^2= ab .

If the vectors ahat (i) + a hat (j) + c hat (k) , hat (i) + hat (k) and c hat (i) + c hat (j) + b hat (k) be coplanar, show that c^(2) = ab

If the vectors ahat(i)+ahat(j)+chat(k),hat(i)+hat(k) and chat(i)+chat(j)+bhat(k) are coplanar then show that c^(2)=ab

(a.hat i ) hat i + ( a. hat j) hat j + (a.hat k) hat k =

Let vec alpha=ahat i+bhat j+chat k,vec beta=bhat i+chat j+ahat k and vec gamma=chat i+ahat j+bhat k are three coplanar vectors with a!=b, and vec v=hat i+hat j+hat k . Then v is perpendicular to vec alpha b.vec beta c.vec gamma d.none of these

If the vectors (ahat(i)+a hat(j)+chat(k)), (hat(i)+hat(k)) and (c hat(i)+c hat(j)+b hat(k)) be coplanar, show that c^(2)=ab .