Final answer:
The vector with initial point (5,3,-4) and terminal point (-3, 12, 5) is å = (-8, 9, 9). To find the unit vector in the direction of å, divide each component by its magnitude, resulting in approximately (-0.5164, 0.5806, 0.5806).
Step-by-step explanation:
To find the vector å with an initial point (5,3,-4) and a terminal point (-3, 12, 5), we subtract the coordinates of the initial point from the coordinates of the terminal point. The vector å can be represented as å = (-3-5, 12-3, 5-(-4)), which simplifies to å = (-8, 9, 9).
Next, to find a unit vector in the direction of å, we divide each component of å by its magnitude. The magnitude of å, denoted as |å|, is the square root of the sum of the squares of its components, which is sqrt( (-8)^2 + 9^2 + 9^2 ) or approximately 15.4919. The unit vector in the direction of å is thus given by each component of å divided by 15.4919, resulting in (-8/15.4919, 9/15.4919, 9/15.4919) or approximately (-0.5164, 0.5806, 0.5806).