Question

The resultant of two vectors is perpendicular to one
of them and has the magnitude 4 m. If the sum of
the magnitude of two vectors is 8 m then their
respective magnitude are
(1) 4 m, 4 m
(2) 2 m, 6 m
(3) 3 m, 5 m
(4) 1 m, 7 m
Ratio of angular sneed of eanan.​

Answer 1

Solution:

Let A and B are the two vectors.

Given:

$\implies$ |A| + |B| = 8 - - - - (1)

And:

|A| + |B| = √{|A|² + |B|² + 2|A|.|B|cosθ}

$\implies$ |A| + |B| = 4 - - - - (2)

Also:

$\implies$ A.(A + B) = 0 or, B.(A + B) = 0

$\implies$ A.(A + B) = 0

$\implies$ or, |A|² + A.B = 0

$\implies$ or, -|A|² = A.B = |A|.|B|cosθ,

Where θ is angle between A and B.

So:

$\implies$ cosθ = -|A| / |B|

Now, from equation (2):

$\implies$ √{|B|² - |A|²} = 4

Squaring both the sides,

$\implies$ |B|² - |A|² = 16

$\implies$ or, (|B| - |A|})(|B| + |A|) = 16

From equation (1),

(|B| - |A|) × 8 = 16

(|B| - |A|) = 2 - - - - (3)

From equations (1) and (3),

|B| = 5 and |A| = 3

Hence,

Correct option: (3) 3 m, 5 m

_________________

Answered by: Niki Swar, Goa❤️

Answer 2

Answer:option (c) is correct

Explanation:

Given:A+B=8...........(1)

|R|^2=A^2 +B^2+2ABcosø.....(2)

We know...

tanø=Bsinø/A+Bcosø

tan90°=Bsinø/A+Bcosø ....(as both are perpendicular)

0=A+Bcosø

-A/B=cosø........3

By solving all three equation we get

A=3m and B=5m