x-अक्ष से बिंदु (1, 4, 3) की लंबवत दूरी क्या है?

  1. 4
  2. 5
  3. \(\sqrt 7\)
  4. 9

Answer (Detailed Solution Below)

Option 2 : 5
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अवधारणा:

xyz-दिक्स्थान में दो बिंदुओं P(x1, y1, z1) और P2(x2y2, z2) के बीच की दूरी दूरी सूत्र के निम्नलिखित सामान्यीकरण द्वारा दी गई है, d(P1, P2) = \(\rm \sqrt {(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\)

गणना:

अत: दिया गया बिंदु = (1, 4, 3)

अब, यदि बिंदु x-अक्ष के लंबवत है तो x-अक्ष निर्देशांक समान होगा,

अत: वह बिन्दु जहाँ से (1, 4, 3) लम्बवत होगा = (1, 0, 0)

तो, लंबवत दूरी d = \(\rm \sqrt {(1-1)^2+(4-0)^2+(3-0)^2}\)

∴ d = \(\rm \sqrt {16+9} =\sqrt {25}\)

∴ d = 5 इकाई

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