Question

Find a vector normal to (8,0,4) and (-7,3,1).

Choose the correct answer below.
A. (-12,-36,24)
B. (12,-36,24)
C. (-12,36,24)
D. (-12,36,-24)

Answer 1

The vector normal to (8,0,4) and (-7,3,1) is found by calculating the cross product and it results in (-12, 36, 24), which is option C.

Step-by-step explanation:

To find a vector normal to two given vectors, we can use the cross product. In this question, we want to find a vector that is normal to both (8,0,4) and (-7,3,1). The cross product of these two vectors can be computed as follows:

1. Calculate the determinant of the matrix formed by the unit vectors i, j, and k in the first row, the components of the first vector in the second row, and the components of the second vector in the third row.
2. The i component (determinant involving the j and k rows):
   (0)(1) - (4)(3) = -12
3. The j component (determinant involving the i and k rows; note the change in sign):
   (8)(1) - (4)(-7) = 8 + 28 = 36
4. The k component (determinant involving the i and j rows):
   (8)(3) - (0)(-7) = 24

By doing this, we find that the normal vector is (-12, 36, 24), which is option C.