The maximum and minimum magnitudes of the resultant of two given vectors are 17 units and 7 units respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is:

Question

The maximum and minimum magnitudes of the resultant of two given vectors are 17 units and 7 units respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is: (A) 14 (B) 16 (C) 18 (D) 13

Tardigrade Admin · Accepted Answer

P+Q=17 ...(1) P-Q=7 ...(2) ∴ P=12,Q=5 Hence, R=√P2+Q2+2PQ cos θ =√(12)2+(5)2+0 (∵ θ =90° ) =13 units

Q. The maximum and minimum magnitudes of the resultant of two given vectors are 17 units and 7 units respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is:

14

16

18

13

12

$P + Q = 17$ ...(1) $P - Q = 7$ ...(2) $∴$ $P = 12, Q = 5$ Hence, $R = P^{2} + Q^{2} + 2 PQ cos θ$ $= (12)^{2} + (5)^{2} + 0$ $(∵ θ = 90^{\circ})$ =13 units

Q. The maximum and minimum magnitudes of the resultant of two given vectors are 17 units and 7 units respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is:

14

16

18

13

12

P+Q=17 ...(1) P−Q=7 ...(2) ∴ P=12,Q=5 Hence, R=P2+Q2+2PQcosθ​ =(12)2+(5)2+0​ (∵θ=90∘) =13 units

$P + Q = 17$ ...(1) $P - Q = 7$ ...(2) $∴$ $P = 12, Q = 5$ Hence, $R = P^{2} + Q^{2} + 2 PQ cos θ$ $= (12)^{2} + (5)^{2} + 0$ $(∵ θ = 90^{\circ})$ =13 units