The projection of point P(→p) on the plane →r⋅→n=q is (→s), then:
A
→s=(q−→p⋅→n)→n∣→n∣2
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B
→s=→p+(q−→p⋅→n)→n∣→n∣2
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C
→s=→p−(→p⋅→n)→n∣→n∣2
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D
→s=→p−(q−→p⋅→n)→n∣→n∣2
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Solution
The correct option is B→s=→p+(q−→p⋅→n)→n∣→n∣2 The equation of line passing through →p and perpendicular to plane be →r.→n=q is →r=→p+t→n Let point of intersection of the plane with the line be →s=→p+t→n Since, S lies on the plane →r.→n=q Therefore, (→p+t→n).→n=q ⇒t=q−→p.→n|n|2 ⇒→s=→p+t→n=→p+((→q−→p⋅→n)∣→n∣2)→n