Question

05. Resultant of two vectors is 7 and it is perpendicular to one of the vector. If greatest
resultant of the two vectors is 49 then find magnitudes of the vectors.​

Answer 1

Answer:

24, 25

Explanation:

Let the two vectors be A and B and the angles between them be Ø.

If 7 is the resultant of the two vectors, then

• 7 = √(A²+B²+2AB.cosØ)

=> 49 = A²+B²+2AB.cosØ. [ squaring both sides]

If the angle between two vectors is 0°, the resultant will be the maximum.

When Ø = 0°,

49= √(A²+B²+2AB.cos0°)

=> 49 = √(A²+B²+2AB)

=> 49 = √(A+B)²

=> 49 = A+B ... i

Now, it is given that the resultant is perpendicular to one of the two vectors.

Let, the resultant be perpendicular to A vector.

So, A²+7² = B²

=> B²–A² = 49

=> (B+A)(B–A) = 49

=> 49.(B–A) = 49 ...( from eq. i)

=> (B–A) = 1 .... ii

From i+ii,

• A+B+B–A = 49+1

=> 2B = 50

=> B = 25

From equation i,

49 = A+25

=> A = 24

So, the magnitude of the two vectors are 24 and 25.