Express the vector `vec(a) = 5 hat (i) - 2 hat (j) + 5 hat (k) ` as sum of two vectors such that one is parallel to the vector `vec(b) = 3 hat(i) + hat (k) ` and the other is perpendicular to `vec(b)`

Find the unit vector in the direction of the vector vec a= hat i+ hat j+ 2 hat k .

Let vec ( a) = hat (i) + 4 hat (j) + 2 hat (k), vec (b) = 3 hat(i) - 2 hat (j) - 7 hat (k) and vec (c ) = 2 hat (i) - hat (j) + 4 hat (k) . Find a vector vec (d) which is perpendicular to both vec (a) and vec (b) and vec ( c) . vec(d) = 18

Let vec (a) = 2 hat (i) - 2 hat (j) + hat (k) , vec (b) = hat (j) - hat (k) and vec(c ) = - hat (i) + 3 hat (j) + 2 hat (k) be three given vectors .Find (vec(a) - 2 vec(b)) xx vec(c)

Let vec (a) = 2 hat (i) - 2 hat (j) + hat (k) , vec (b) = hat (j) - hat (k) and vec(c ) = - hat (i) + 3 hat (j) + 2 hat (k) be three given vectors .Find angle between vec(a) and vec(b)

Let vec (a) = 2 hat (i) - 2 hat (j) + hat (k) , vec (b) = hat (j) - hat (k) and vec(c ) = - hat (i) + 3 hat (j) + 2 hat (k) be three given vectors .Find vec(a) xx vec(b)

If vec(a) = 3 hat (i) + 4 hat (j) - hat(k) , vec(b) = hat(i) - 3 hat (j) + 4 hat (k) and vec (c ) = 5 hat (i) - 6 hat (j) + 4 hat (k) , find the vector vec (r ) which is perpendicular to both vec(a) and vec(b) and which satisfies the relation vec(r).vec(c ) = 91

For given vector, vec a = 2 hat i j +2 hat k and vec b = - hat i + hat j - hat k , find the unit vector in the direction of the vector vec a + vec b .

Let vec (a) = 2 hat (i) - 2 hat (j) + hat (k) , vec (b) = hat (j) - hat (k) and vec(c ) = - hat (i) + 3 hat (j) + 2 hat (k) be three given vectors .Find (vec(a) + vec(b)) xx (vec(b)- vec(c ))

If the vectors vec (a) = 2 hat (i) - hat (j) + hat (k) , vec ( b) = hat (i) + 2 hat (j) - 3 hat (k) and vec(c ) = 3 hat (i) + lambda hat (j) + 5 hat (k) are coplanar , find the value of lambda

Let vec (a) = 2 hat (i) - 2 hat (j) + hat (k) , vec (b) = hat (j) - hat (k) and vec(c ) = - hat (i) + 3 hat (j) + 2 hat (k) be three given vectors .Find vec(c ) xx (-vec(a))