Final answer:
To find the value of x so that vector B is perpendicular to vector A, the dot product of A and B must be equal to zero. The values of x that satisfy this condition is x = 5. The perpendicular relationship between vectors A and B means that the two vectors are oriented at a right angle to each other.
Step-by-step explanation:
To find the value of x so that vector B is perpendicular to vector A, we need to determine the dot product of A and B. For two vectors to be perpendicular, their dot product must be equal to zero.
Given that A = 2i - 6j and B = 3xi + 5j, the dot product is:
A · B = (2)(3x) + (-6)(5) = 6x - 30 = 0
Solving this equation gives us x = 5. So, B = 3(5)i + 5j.
The perpendicular relationship between vectors A and B means that the two vectors are oriented at a right angle to each other. This is represented by the dot product of A and B being zero. It indicates that the vectors do not share any parallel component.
If the magnitude of A is 8 units, we can find the magnitude of B using the equation:
|B| = |A| * sin(theta)
Since the angle between A and B is 90 degrees (perpendicular), we have:
|B| = 8 * sin(90)
|B| = 8
To graphically represent vectors A and B on a coordinate plane, we can plot the vectors as arrows. Vector A would start at the origin (0, 0) and reach (2, -6) units, while vector B would start at the origin and reach (15, 5) units. The two arrows would be oriented at a right angle to each other.