Answer:
(a) 10√2 cm
(b) -135°
(c) 20 cm
(d) 90°
(e) 0
(f) 0 (any)
Step-by-step explanation:
(a, b) At 1/4 past the hour, the minute hand points to "3" on the clock face. Its angle relative to the +x axis is 0°.
At 1/2 past the hour, the minute hand points to "6" on the clock face. Its angle relative to the +x axis is -90°. The positions of the two hands and the vector between 3 and 6 form an isosceles right triangle whose hypotenuse is 10√2 cm in length.
The internal acute angles of that triangle are 45°. The external angle of that triangle at "3" is the angle the vector from "3" to "6" makes with the +x axis. Measured from the +x axis, it is -135°.
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(c, d) The displacement from straight down to straight up is twice the length of the minute hand, 20 cm. The angle is straight up, 90°.
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(e, f) The net displacement after 1 hour is zero. The minute hand is in the same (straight up) position it was an hour ago. (The angle can be anything you like, as it is irrelevant when the magnitude is zero.)
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A diagram may help you visualize these clock hand positions.
