Dot product of a vector with vectors and are respectively 4, 0 and 2. Find the vector.

Vectors:

Their Dot products are 4, 0 and 2.

Calculation:

Let the required vector be,

Now,

x - y + z = 4 …Eq. 1

Similarly

2x + y - 3z = 0 …Eq. 2

x + y + z = 2 …Eq. 3

Subtract Eq. 1 from Eq. 3

(x + y + z) – (x - y + z) = 2 - 4

⇒ 2y = -2

y = - 1

Now putting the value of y in equation(2) and equation (3) we get,

2 x – 3 z = 1 …(Eq(4))

x + z = 3 ……(Eq(5))

Eq(4) – 2 × Eq (5)

- 5 z = - 5

z = 1

Now putting value of z in equation (1) we get,

x – y + z = 4

x + 1 + 1 = 4

x = 2

So the vector is,