The resultant R⃗=P⃗+Q⃗ is perpendicular to P⃗. If the magnitudes are P and Q and θ is the angle between P⃗ and Q⃗, which relation must hold?
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Question

The resultant R⃗=P⃗+Q⃗ is perpendicular to P⃗. If the magnitudes are P and Q and θ is the angle between P⃗ and Q⃗, which relation must hold?

G1 Physics · Accepted Answer

Resolve Q⃗ along P⃗. For R⃗ to be perpendicular to P⃗, its component along P⃗ must vanish: P+Q cosθ=0, so P=−Q cosθ.