For any vector `x`, the value of `(vecx×hati)^2+(vecx×hatj)^2+(vecx×hatk)^2` is equal to

For many vector vecx , the value of (vecx xxhati)^2+(vecx xxhatj)^2+(vecx xxhatk)^2 is equal to

Four vectors veca, vecb, vecc and vecx satisfy the relation (veca.vecx)vecb=vecc+vecx where vecb.veca ne 1 . The value of vecx in terms of veca, vecb and vecc is equal to

Four vectors veca, vecb, vecc and vecx satisfy the relation (veca.vecx)vecb=vecc+vecx where vecb.veca ne 1 . The value of vecx in terms of veca, vecb and vecc is equal to

Let vecx be a vector in the plane containing vectors veca=2hati-hatj+hatk and vecb=hati+2hatj-hatk . If the vector vecx is perpendicular to (3hati+2hatj-hatk) and its projection on veca is (17sqrt(6))/(2) , then the value of |vecx|^(2) is equal to __________.

If c is a given non - zero scalar, and vecA and vecB are given non- zero , vectors such that vecA bot vecB . Then find vector, vecX which satisfies the equations vecA.vecX =c and vecA xx vecX =vecB .

If c is a given non - zero scalar, and vecA and vecB are given non- zero , vectors such that vecA bot vecB . Then find vector, vecX which satisfies the equations vecA.vecX =c and vecA xx vecX =vecB .

If c is a given non - zero scalar, and vecA and vecB are given non- zero , vectors such that vecA bot vecB . Then find vector, vecX which satisfies the equations vecA.vecX =c and vecA xx vecX =vecB .

Find the value of |vecx| if for a unit vector a (vecx-veca)(vecx+veca)=8

Find |vecx|, if for a unit vector veca, (vecx-veca).(vecx+veca) = 12 .