Question

A vector A makes an angle of 20 degrees and B makes an angle of 110 degree with x-axis. The magnitude of these vectors are 3 m and 4 m respectively. Find the resultant

Answer 1

A⃗ A→ & B⃗ B→ make angles 20∘20∘ & 110∘110∘ with the x-axis hence the angle between the vectors θ=110−20=90∘θ=110−20=90∘

Now, the resultant of two vectors A⃗ A→ & B⃗ B→ at an angle θ=90∘θ=90∘

R=|A⃗ |2+|B⃗ |2+2|A⃗ ||B⃗ |cosθ−−−−−−−−−−−−−−−−−−−−√R=|A→|2+|B→|2+2|A→||B→|cos⁡θ

=302+42+2(30)(4)cos90∘−−−−−−−−−−−−−−−−−−−−−√=302+42+2(30)(4)cos⁡90∘

=2229−−−√=2229

Now, angle (αα) of resultant with B⃗ B→ is given as

tanα=|A⃗ ||B⃗ |tan⁡α=|A→||B→|

tanα=404tan⁡α=404

α=tan−1(10)≈84.28940686250037∘α=tan−1⁡(10)≈84.28940686250037∘

& the angle of the resultant with the x-axis is

=110∘−α=110∘−tan−1(10)

Answer 2

r= root ..Asquare +B square +2AB cos theta
here
A=3m
B=4m
theta=110-20=90(because it making angle with +'ve c axis.
= root.9+16+2×3×4×0
=..root.25
=5 m.
hope it help u.