Find the value of `lambda` so that the vectors `vec(A) = 2hati + lambda hatj +hatk` and `

Find the value of lambda such that vectors veca = 2hati + lambda hatj + hatk and vecb = hati + 2hatj + 3hatk are orthogonal.

Find the value of lambda in the unit vector 0.4 hati + 0.8 hatj + lambda hatk .

The value of ‘ lambda ’ so that the vectors hati - 3̂ hatj + hatk , 2̂ hati + lambda hatj + hatk and 3 hati + hatj - 2 hatk are coplanar, will be

Find unit vector parallel to the resultant of the vectors vec(A) = hati +4hatj +2hatk and vec(B) = 3hati - 5hatj +hatk .

Find the value of m so that the vector 3 hati - 2hatj +hatk is perpendicular to the vector. 2hati +6hatj +m hatk .

Find the angle between the vectors vec(A) = 2 hati - 4hatj +6 hatk and vec(B) = 3 hati + hatj +2hatk .

Find the value of 'm' for which the line vec(r) = ( hati + 2 hatk ) + lambda (2 hati - m hatj - 3 hatk) is parallel to the plane vec(r).(m hati + 3 hatj + hatk ) = 4.

Find the area of the triangle formed by the tips of the vectors vec(a) = hati - hatj - 3hatk, vec(b) = 4hati - 3hatj +hatk and vec(c) = 3 hati - hatj +2 hatk .

Find the angle between the vectors vec A = hati + hatj + hatk and vec B =-hati - hatj + 2hatk .