Question

A vector A makes an angle of 20 degree and vector B make an angle of 110 degree with the x axis the magnitude of these vector are 3m and 4m respectively. Find the resultant
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Answer 1

Answer:

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

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

R=|A⃗ |2+|B⃗ |2+2|A⃗ ||B⃗ |cosθ−−−−−−−−−−−−−−−−−−−−√

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

=2229−−−√

Now, angle (α) of resultant with B⃗ is given as

tanα=|A⃗ ||B⃗ |

tanα=404

α=tan−1(10)≈84.28940686250037∘

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

=110∘−α=110∘−tan−1(10)