Question

Q) Two Vectors having equal magnitude of 5 units, have an angle of 60 between them. Find the magnitude of their resultant vector and its angle from one of the vectors: (solve by component method)

Answer 1

$Magnitude \: of \: resultant \: vector$

$R = \sqrt{ {A}^{2} + {B}^{2}2 \: ( A) \: (B) \cos60 }$

$R = \sqrt{25 + 25 + 2 \times 25 \times \frac{1}{2} }$

$R = \sqrt{75}$

$R = 8.66$

$For \: angle,∠ = {tan}^{ - 1} ( \frac{B \sinθ }{A + B \cosθ} )$

$∠ = {tan}^{ - 1} ( \frac{5 \times \frac{ \sqrt{3} }{2} }{5 + 5 \times \frac{1}{2} })$

$∠ = {tan}^{ - 1} ( \frac{1}{ \sqrt{3} } )$

$∠ = {30}^{0}$

I hope this will help you dear..

Always stay safe and stay healthy..

Answer 2

Step-by-step explanation:

Let 5he vectors be a and b.

|a - b|² = (a - b). (a - b)

= |a|² + |b|² - 2a.b (noting that a.b = b.a))

= 25 + 25 - 2 x 5 x 5 cos60°

= 50 - 50 x (1/2) = 25.

So |a - b| = 5.