XI - 2.3 Addition of vectors - Video Lectures

Addition of vectors

Magnitude of a^v+b^v = SQRT(a²+b²+ 2ab cos θ)

The angle of the resultant with a^v 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
and
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)
PhysicsEH
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