Question

Vector perpendicular to plane through a(1,0,0) b(2,0,-1) and c(1,4,3)?

Answer 1

To find the vector perpendicular to the plane through points A(1,0,0), B(2,0,-1), and C(1,4,3), it is necessary to calculate the cross product of vectors AB and AC, resulting in the vector (4, -3, 4).

Step-by-step explanation:

To find the vector perpendicular to the plane through points A(1,0,0), B(2,0,-1), and C(1,4,3), we first need to find two vectors that are parallel to the plane by subtracting the coordinates of these points. Let's consider vectors AB and AC:

AB = B - A = (2, 0, -1) - (1, 0, 0) = (1, 0, -1)

AC = C - A = (1, 4, 3) - (1, 0, 0) = (0, 4, 3)

Now, the cross product of AB and AC will give us a vector that is perpendicular to the plane. The cross product, AB x AC, is:

i(0*3 - 4*-1) - j(1*3 - 0*-1) + k(1*4 - 0*0)

i(0 + 4) - j(3 - 0) + k(4 - 0)

i(4) - j(3) + k(4)

Therefore, the vector perpendicular to the plane is (4, -3, 4).