Calculate, correct to one decimal place, the angle between 5i + 12j and -2i +…

Calculate, correct to one decimal place, the angle between 5i + 12j and -2i + 3j.

Correct Answer: Option B

Explanation

(a . b = |a||b|cos theta)

((5i + 12j).(2i + 3j) = -10 + 36 = 26)

(26 = |5i + 12j||-2i + 3j|cos theta)

(|5i + 12j| = sqrt{5^{2} + 12^{2}} = sqrt{25 + 144} = 13)

(|2i + 3j| = sqrt{2^{2} + 3^{2}} = sqrt{4 + 9} = sqrt{13})

(26 = 13(sqrt{13})cos theta)

(cos theta = frac{26}{13sqrt{13}} = 0.5547)

(theta = 56.3°)