If `vec(a) = hat(i) - hat(j) + 7hat(k)` and `vec(b) = 5 hat(i) + lambda hat(k)`, then find the value of `lambda` so that the vectors `vec(a) + vec(b) ` and `vec(a) - vec(b)` are orthogonal .

If vec(a)=3hat(i)+hat(j)+9hat(k) and vec(b)=hat(i)+lambda hat(j)+3hat(k) , then find the value of 'lambda' for which the vectors (vec(a)+vec(b)) and (vec(a)-vec(b)) are perpendicular to each other.

If vec(a)=5hat(i)-hat(j)+7hat(k) and vec(b)=hat(i)-hat(j)-lambda hat(k) , find the value of lambda for which (vec(a)+vec(b)) and (vec(a)-vec(b)) are orthogonal.

If vec(a) = hat(i) + hat(j) + 2 hat(k) and vec(b) = 3 hat(i) + 2 hat(j) - hat(k) , find the value of (vec(a) + 3 vec(b)) . ( 2 vec(a) - vec(b)) .

If vec(a) = 2hat(i) + hat(j) - hat(k) and vec(b) = hat(i) - hat(k) , then projection of vec(a) on vec(b) will be :

If vec(a) = 5 hat(i) - hat(j) - 3 hat(k) and vec(b) = hat(i) + 3 hat(j) - 5 hat(k) , find the angle between vec(a) and vec(b) .

If vec(a) = hat(i) + 2 hat(j) + 3 hat(k) and vec(b) = 2 hat(i) + 3 hat(j) + hat(k) , find a unit vector in the direction of ( 2 vec(a) + vec(b)) .

If vec a=widehat a=hat i-hat j+7hat k and vec b=5hat j-hat j+lambdahat k, then find the value of lambda so that vec a+vec b and vec a-vec b are perpendicular vectors.

If vec(a)=4hat(i)-hat(j)+hat(k) and vec(b)=2hat(i)-2hat(j)+hat(k) , then find a unit vector parallel to the vector vec(a)+vec(b) .

If vec(a)= hat(i) - 2hat(j) + 5hat(k) and vec(b) = 2hat(i) + hat(j) -3hat(k) , then (vec(b) - vec(a)).(3 vec(a) +vec(b)) equal to?

If vectors vec(a) = 3 hat(i) + hat(j) - 2 hat(k) and vec(b) = hat(i) + lambda(j) - 3 hat (k) are perpendicular to each other , find the value of lambda .