A vector P directed along the X -axis is added to vector Q which has a magnitude of 10 ~m . The resultant vector is directed along the Y -axis, with a magnitude that is 2 times that of P . The magnitude of P is

Step-by-step solution

By parallelogram law of vector addition, angle made by resultant with P is given by; = Q P+Q Here =90^ so ; 90^ = = Q P+Q P+Q =0 or Q =-P Now, magnitude of resultant, R= P^2+Q^2+2 P Q Here, we have R=2 P and Q =-P and Q=10 ~m So, 2 P= P^2+100-2 P^2 4 P^2=100-P^2 5 P^2=100 or P= 20 =2 5 ~m Magnitude of P is 2 5 ~m