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RBSE Solutions for Class 12 Maths Chapter 14 त्रि – विमीयज्यामिति Ex 14.1

May 24, 2019 by Prasanna Leave a Comment

   

Rajasthan Board RBSE Class 12 Maths Chapter 14 त्रि – विमीयज्यामिति Ex 14.1

प्रश्न 1.
एक रेखा के दिक्-कोसाइन ज्ञात कीजिए जो निर्देशाक्षों के साथ समान कोण बनाती हैं।
हल :
माना रेखा निर्देशांक्षों के साथ समान कोण θ बनाती है। अतः दिक्-कोसाइन
l = cos θ, m = cos θ, n = cos θ
परन्तु
l² + m² + n² = 1
⇒ cos² θ + cos² θ + cos² θ = 1
⇒ 3 cos² θ = 1
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.1

प्रश्न 2.
दो बिन्दुओं (4, 2, 3) तथा (4, 5, 7) को मिलाने वाली सरल रेखा की दिक्-कोज्याएँ ज्ञात कीजिए।
हल :
बिन्दुओं P(x1, y1, z1) तथा Q(x2, y2, z2) को मिलाने वाली रेखा के दिक्-कोसाइन
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.1

प्रश्न 3.
यदि एक रेखा के दिक्-अनुपात 2, -1, -2 हैं, तो इसकी दिक्-कोज्याएँ ज्ञात कीजिए।
हल :
दिया है : a = 2, b = -1, c = -2
माना रेखा के दिक्-कोसाइन l, m और n हैं तो
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.1

प्रश्न 4.
एक सदिश \(\vec { r } \), X, Y तथा Z-अक्षों के साथ क्रमशः 45°, 60°, 120° के कोण बनाता है। यदि सदिश \(\vec { r } \) का परिमाण 2 इकाई है तो \(\vec { r } \) ज्ञात कीजिए।
हल :
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.1

RBSE Solutions for Class 12 Maths

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