Suppose the hands on a clock are vectors, where the hour hand has a length of 2 and the minute hand has a length of 4. What is the dot product of these two vectors when the clock reads 2 o'clock?

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Solution

When the clock reads 2 o'clock, the angle between the minute hand and the hour hand will be 60 $^{0}$ .
Thus, the dot product will be $= 4 \times 2 \times c o s 60^{0} = 4 \times 2 \times \frac{1}{2} = 4$

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Suppose the hands on a clock are vectors, where the hour hand has a length of 2 and the minute hand has a length of 4. What is the dot product of these two vectors when the clock reads 2 o'clock?

When the clock reads 2 o'clock, the angle between the minute hand and the hour hand will be 600.Thus, the dot product will be =4×2×cos600=4×2×12=4

When the clock reads 2 o'clock, the angle between the minute hand and the hour hand will be 60 $^{0}$ .
Thus, the dot product will be $= 4 \times 2 \times c o s 60^{0} = 4 \times 2 \times \frac{1}{2} = 4$