If then

The correct answer is:

The given vector is
.
The given conditions are

Let the vector b be 
We will find the dot product and cross product.


We will add all three equations.
3z - y + 2z - x + 2y - 3x = 7 + 3 - 5
5z + y - 4x = 5               ...(4)
We will denote dot product by equation (5)
2x + 3y + z = 1                 ...(5)
We will multiply it by (2) and add it to (4)
5z + y - 4x + 2(2x + 3y + z) = 5 + 2(1)
5z + y - 4x + 4x + 6y + 2z = 7
7z + 7y = 7
z + y = 1            ...(6)
We will add equation (1) to (6)
3z - y + z + y = 7 + 1
4z = 8
z = 2
We will substitute this in equation (6)
z + y = 1
2 + y = 1
y = - 1
We will substitute this in equation (3)
2y - 3x = -5
2(-1) - 3x = -5
-3x = -3
x = 1
The values are x = 1, y = -1, z = 2
So,

This is the value of the vector.

For such questions, we should know how to find the dot product and cross product. Dot product of two vectors is always a scalar quantity. The cross product of two vectors is a vector quantity.