Sunday, May 8, 2016
XI - 2.3 Addition of vectors - Video Lectures
Addition of vectors
Magnitude of av+bv = SQRT(a²+b²+ 2ab cos θ)
The angle of the resultant with av is α where
tanα = b sin θ/(a+b cos θ)
Interesting point to make note of:
Two vectors having equal magnitudes of a make an angle θ with each other. Find the magnitude and direction of the resultant(Resultant is output of the addition of two vectors.)
Magnitude = 2a cos θ/2
tan α = a sin θ/(a + a cos θ) = (2asin(θ/2)cos(θ/2))/(2acos²(θ/2))
= tan (θ/2)
Example: Two vectors are of equal magnitude of 10 units. One of them is inclined at 45° to the X-axis and the other is inclined at 75° to the X-axis. Find the magnitude and direction of the resultant with respect to X-axis.
The angle between vectors is 30°.
Hence magnitude of the resultant will be 20 cos 15°
The direction - The resultant is inclined at 60° to the X axis.
Physics Vector Addition (Algebraic)