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

Options

A. 14
B. 16
C. 18
D. 13

Answer

D

Explanation

Let `vecP and vecQ` be two vectors. The. according to question
`|vecP+vecQ|=17 " or " P+Q = 17 " "....(i)`
`|vecP-vecQ|=7 " or " P-Q = 7 " "....(ii)`
On adding and subtracting the equations (i) and (ii) we get
P = 12 , Q = 5
Magnitude of resultant is given by
`R = [P^(2) +Q^(2) + 2PQ cos theta]^(1//2)`
Substituting the values of P and Q , we get
R = 13