Question

why do we take theta as 180 to solve the equation in this question.plz explain

Answer 1

Your answer is ----

Let the two vector be A and B .

Since , maximum and minimum magnitude of the resultant of two vectors are 17 and 7 respectively .

we kown that for maximum magnitude angle between two vectors is 0°

So, √A^2+B^2+2ABcos@ = 17

=> √A^2+B^2+2ABcos0° = 17

=> √A^2+B^2+2AB = 17 [ °•° cos0° = 1 ]

=> A+B = 17 .........(1)

we also knoe that for minimum magnitude angle between two vector is 180°.


So, √A^2+B^2+2ABcos180° = 7

=> √A^2+B^2-2AB = 7 [ °•° cos180° = -1 ]

=> A - B = 7 .......(2)

adding equation (1) & (2) , we get

2A = 24

=> A = 24/2

=> A = 12

put this value in equation (1) , we get

12 + B = 17

=> B = 5

Such that , vector A = 12 and B = 5

Since , angle between both vector is 90°.

Therefore ,

|A+B| = √A^2+B^2+2ABcos90°

= √12^2+5^2 [ °•° cos90° = 0 ]

= √169 = 13

Hence , magnitude of their resultant is 13

option (d) is right


we take 180° because magnitude of two vectors is minimum only when angle between them is 180°



【 Hope it helps you 】