The ratio in which the line joining (3,4,−7) and (4,2,1) is dividing the xy-plane

Engineering

Mathematics

Equation of Straight Line in 3D

Section Formulae and Centres of a Triangle

Distance from a Plane

Question

The ratio in which the line joining (3,4,−7) and (4,2,1) is dividing the xy-plane

7:1

2:1

3:4

4:3

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Let the given points be

A(3,4,−7), B(4,2,1)

Let a point on XY−plane be P(x,y,0) and the line AB in the ratio k:1

then by section formula

0 = \frac{k \times 1 + 1 \times - 7}{k + 1}

k – 7 = 0

k = 7

Therefore, ratio is 7 : 1

Hence, option C is correct.