Question

Two vectors of magnitude 4 units each ,subtending an angle theta between them has resultant equal to 4 units. If the angle between them is increased by 60 degree the resultant becomes

Answer 1

put thetha = 60+theta in resutant formula

Answer 2

Answer: The Resultant becomes 0.

Resultant of 2 Vectors: $R^2 = A^2+B^2+2ABcos\beta \alpha$ where R is the Resultant of Vectors A and B and α is the angle between them.

Explanation:

Step 1: Given Data

• R = 4
• A = 4 and B = 4
• Let the angle between A and B be $\alpha$

Step 2: Initial angle between A and B

$R^2 = A^2 + B^2 +2ABcos\alpha \\4^2 = 4^2+4^2+2X4X4Xcos\alpha \\\alpha = cos^{-1}(\frac{16-32}{32})\\\alpha = cos^{-1}(-0.5) = 120$

Step 3: Resultant when α = 120 + 60 = 180

$R^2 = A^2+B^2+2ABcos\beta \alpha\\R^2=4^2+4^2+2X4X4Xcos180\\R= \sqrt{16+16-32}\\R=0$

The resultant changes to 0