Question 31

Mathematics Scalar and Vector Products Hard

Two forces F<sub>1</sub> and F<sub>2</sub> are used to pull a car, which met an accident. The angle between the two force is&nbsp;&theta;. Find the value of&nbsp;&theta; for the resultant force is equal to&nbsp;<span class="math-tex">\(\sqrt{(F_1^2 + F_2^2)}\)</span>

(A) &theta; = 0
(B) &theta; = 45
(C) &theta; = 90
(D) &theta; = 125
View Dynamic Solution & Explanation
Correct Solution: Option C

Step-by-step Solution:

The resultant force of two vectors \( F_1 \) and \( F_2 \) is: \[ \sqrt{F_1^2 + F_2^2 + 2 F_1 F_2 \cos \theta} \] When \( \theta = 90^\circ \), the resultant force becomes: \[ \sqrt{F_1^2 + F_2^2} \] Thus, when \( \theta = 90^\circ \), the resultant force is given by the above expression.