If `a=5hati-hatj+7hatk and b=hati-hatj+lamdahatk`, then find `lamda` such that a+b and a-b are orthogonal.

If veca=5hati-hatj+7hatk and vecb=hati-hatj+lamda hatk, find lamda such that veca+vecb and veca-vecb are orthogonal

If a=2hati-hatj+2hatk and b=-hati+hatj-hatk , then find a+b. Also, find a unit vector along a+b.

If a =2hati+3hatj+4hatk and b =4hati+3hatj +2hatk ,find the angel between a and b.

If a=hati+2hatj+2hatk and b=3hati+6hatj+2hatk , then find a vector in the direction of a and having magnitude as |b|.

If a=2hati+2hatj-8hatk and b=hati+3hatj-4hatk , then the magnitude of a+b is equal to

If a=hati+hatj+hatk,b=hati+hatj-hatk , then vectors perpendicular to a and b is/are

If a=3hati-2hatj+hatk,b=2hati-4hatj-3hatk and c=-hati+2hatj+2hatk , then a+b+c is

If a=3hati+hatj-4hatk,b=6hati+5hatj-2hatk, then find the area of a triangle whose adjacent sides are determined by a and b.

The position vectors of the point A, B, C and D are 3hati-2hatj -hatk, 2hati+3hatj-4hatk, -hati+hatj+2hatk and 4hati+5hatj +lamda hatk , respectively. If the points A, B, C and D lie on a plane, find the value of lamda .

If a=hati+4hatj+2sqrt(2)hatk and b=(hati+hatj)sqrt(2) then find component of a perpendicular to b