Gujarat BoardEnglish MediumSTD 12 ScienceMathsThe plane3 Marks
Question
Write the ratio in which the plane 4x + 5y − 3z = 8 divides the line segment joining the points (−2, 1, 5) and (3, 3, 2).
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Answer
We know that the ratio in which the plane ax + by + cz + d = 0 divides the line sebment joining (x1, y1, z1) and (x2, y2, z2) is $\frac{-(\text{ax}_1+\text{by}_1+\text{cz}_1+\text{d})}{\text{ax}_2+\text{by}_2+\text{cz}_2+\text{d}}$ Here, a = 4,b = 5,c = -3,d = -8,x1 = -2,y1 = 1,z1 = 5,x2 = 3,y2 = 3,z2 = 2 So, the required ratio $=\frac{-(4(-2)+5(1)-3(5)-8)}{4(3)+5(3)-3(2)-8}$ $=\frac{-(-8+5-15-8)}{12+15-6-8}$ $=\frac{26}{13}$ $=\frac{2}{1}$ or $2 :1.$
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