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Question: The minimum distance of the point (a, b, c) from x-axis is –...

The minimum distance of the point (a, b, c) from x-axis is –

A

a2+b2\sqrt{a^{2} + b^{2}}

B

c2+a2\sqrt{c^{2} + a^{2}}

C

b2+c2\sqrt{b^{2} + c^{2}}

D

a2+b2+c2\sqrt{a^{2} + b^{2} + c^{2}}

Answer

b2+c2\sqrt{b^{2} + c^{2}}

Explanation

Solution

A point on the x-axis, (x, 0, 0)

distance d = (x−a)2+b2+c2\sqrt{(x - a)^{2} + b^{2} + c^{2}}

̃ d2 = (x – a)2 + b2 + c2

d(d2)dx\frac{d(d^{2})}{dx} = 2(x – a) = 0 ̃ x = a

so dmin = b2+c2\sqrt{b^{2} + c^{2}}