The length of the perpendicular from the point (2, -1, 4) on the straight line, `(x+3)/(10)=(y-2)/(-7)=(z)/(1)` isA. greater than 3 but less than 4B. less than 2C. greater than 2 but less than 3D. greater than 4

The length of the perpendicular from the point (2, -1, 4) on the strai

1.	The length of the perpendicular from the point (2, -1, 4) on the straight line, `(x+3)/(10)=(y-2)/(-7)=(z)/(1)` isA. greater than 3 but less than 4B. less than 2C. greater than 2 but less than 3D. greater than 4
Answer» Correct Answer - A Equation of given line is `(x+3)/(10)=(y-2)/(7)=(z)/(1)=r("let")" "...(i)` Coordinates of a point on line (i) is `A(10r-3,-7r+2,r)` Now, let the line joining the points `P(2, -1, 4)` and `A(10-r-3, -7r+2, r)` is perpendicular to line (i). Then, `PA.(10hati-7hatj+hatk)=0` [`because` vector along line (i) is `(10hati-7hatj+hatk)`] `implies[(10r-5)hati+(-7r+3)hatj+(r-4)hatk].[10hati-7hatj+hatk]=0` `implies10(10r-5)-7(3-7r)+(r-4)=0` `implies100r-50-21+49r+r-4=0` `implies150r=75impliesr=(1)/(2)` So, the foot of perpendicular is `A(2,-(3)/(2),(1)/(2))` [put `r=(1)/(2)` in the coordinatcs of point A] Now, perpendicualr distance of point `P(2, -1, 4)` from the line (i) is `PA=sqrt((2-2)^(2)+(-(3)/(2)+1)^(2)+((1)/(2)-4)^(2))` `=sqrt((1)/(4)+(49)/(4))=sqrt((50)/(4))=(5)/(sqrt(2))` which lies in (3, 4).

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The length of the perpendicular from the point (2, -1, 4) on the straight line, `(x+3)/(10)=(y-2)/(-7)=(z)/(1)` isA. greater than 3 but less than 4B. less than 2C. greater than 2 but less than 3D. greater than 4

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