Question

If a and b are two vectors each of magnitude 5 units if they are inclined with the x axis at angles of 30 degrees and 90 degrees respectively their resultant will be

Answer 1

Answer:

resultant will be 5√3 magnitude & 60° inclined with x axis

Explanation:

If a and b are two vectors each of magnitude 5 units if they are inclined with the x axis at angles of 30 degrees and 90 degrees respectively

a = 5Cos30° i + 5Sin30° j

=> a = 5√3/2 i  + 5/2 j

b = 5Cos90° i + 5 Sin90° j

=> b = 0 i  + 5 j

a + b =  5√3/2 i  + (5/2 + 5)j

=> a + b = 5√3/2 i  + 15/2 j

Resultant Magnitude = √ (5√3/2)² + (15/2)²

=  √ ((75 + 225)/4)

= √75

= 5√3

Tanα = (15/2)/(5√3/2) = √3

=> α = 60°

resultant will be 5√3 magnitude & 60° inclined with x axis