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,