Three vectors OP, OQ and OR each of magnitude A are acting as shown in figure. The resultant of the three vectors is A√x. The value of x i $s _____.$

Question

Three vectors OP, OQ and OR each of magnitude A are acting as shown in figure. The resultant of the three vectors is A√x. The value of x i s _____.

G1 Physics · Accepted Answer

Image Take OP along +x-axis and OQ along +y-axis. OR makes 45° below +x-axis. Therefore: OP = Aî OQ = Aĵ OR = (A/√2)î - (A/√2)ĵ Resultant components: R(x) = A + A/√2 R(y) = A - A/√2 Hence: |R|² = [A + A/√2]² + [A - A/√2]² = 3A² Therefore: |R| = √3 A Given: |R| = A√x Hence: x = 3