Question

Complete the table for two vectors - inclined at angle inclined at angle thita.​

Answer 1

Answer:

⃗ |=AB,|Q⃗ |=AC and |R⃗ |=AD.

AD2=AE2+DE2=(AB+BE)2+DE2

=AB2+2AB.BE+BE2+DE2=AB2+2AB.BE+BD2.

BE=BD.cosθ and BD=AC.

⇒(|R⃗ |)2=(|P⃗ |)2+2(|P⃗ |)(|Q⃗ |)cosθ+(|Q⃗ |)2.

⇒|R⃗ |=(|P⃗ |)2+2(|P⃗ |)(|Q⃗ |)cosθ+(|Q⃗ |)2−−−−−−−−−−−−−−−−−−−−−−−−−−√.

This gives the magnitude of the resultant vector R⃗ .

The angle between R⃗ and P⃗ is ∠DAE=α.

tanα=DEAE=DBsinθAB+BE=|Q⃗ |sinθ|P⃗ |+|Q⃗ |cosθ.

α=arctan(|Q⃗ |sinθ|P⃗ |+|Q⃗ |cosθ).

This gives the direction of the resultant vector R⃗ .

Explanation:

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