Vector A is given by A = c x + 6 y, and vector B is given by B = 4.8 x - 16.2 y, where x and y are the x and y unit vectors. What does c need to be such that these two vectors are perpendicular?
Remeber that perpendicular means that the slopes are negative reciprocals of each other
To determine when two vectors are perpendicular, we can use the dot product. If the dot product of two vectors is zero, it means that the vectors are perpendicular.
So, let's calculate the dot product of vectors A and B.
Vector A = c x + 6 y
Vector B = 4.8 x - 16.2 y
The dot product (A · B) is given by the formula:
A · B = (A_x * B_x) + (A_y * B_y)
In our case, A_x = c, A_y = 6, B_x = 4.8, and B_y = -16.2. Substituting these values into the dot product formula, we get:
A · B = (c * 4.8) + (6 * -16.2)
To make the dot product zero (since we want the vectors to be perpendicular), we need to solve for c:
(c * 4.8) + (6 * -16.2) = 0
Now, let's simplify the equation and solve for c:
4.8c - 97.2 = 0
4.8c = 97.2
c = 97.2 / 4.8
c ≈ 20.25
Therefore, c needs to be approximately 20.25 in order for vectors A and B to be perpendicular.