Three Dimensional Geometry

Question

Find the distance of a point (1, –2, 3) from the plane x – y + z = 5 measured parallel to the line $straight x over 2 space equals space straight y over 3 space equals space fraction numerator straight z over denominator negative 6 end fraction$

Solution

The equation of given plane is
x – y + z = 5 ...(1)
The equation of the line through P (1,–2, 3) parallel to the line $straight x over 2 space equals space straight y over 3 space equals fraction numerator straight z over denominator negative 6 end fraction$ are $fraction numerator straight x minus 1 over denominator 2 end fraction space equals space fraction numerator straight y plus 2 over denominator 3 end fraction space equals space fraction numerator straight z minus 3 over denominator negative 6 end fraction$

Any point on it is Q (2 r + 1, 3 r –2, – 6 r + 3)
Let it lie on plane (1)
∴ 2r + 1 – 3r + 2 – 6r + 3 = 5
$therefore space space space space minus 7 space straight r space equals space minus 1 space space space space space space space space rightwards double arrow space space space straight r space equals space 1 over 7$
$therefore space space space point space straight Q space is space space open parentheses 2 over 7 plus 1 comma space space 3 over 7 minus 2 comma space space fraction numerator negative 6 over denominator 7 end fraction plus 3 close parentheses space space straight i. straight e. space space space open parentheses 9 over 7 comma space minus 11 over 7 comma space 15 over 7 close parentheses$
$therefore space space space required space distance space PQ space equals space square root of open parentheses 9 over 7 minus 1 close parentheses squared plus open parentheses negative 11 over 7 plus 2 close parentheses squared space plus space open parentheses 15 over 7 minus 3 close parentheses squared end root space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space square root of 4 over 49 plus 9 over 49 plus 36 over 49 end root space equals space square root of 49 over 49 end root space equals space 1.$

For Daily Free Study Material Join wiredfaculty

Three Dimensional Geometry

Find the distance of a point (1, –2, 3) from the plane x – y + z = 5 measured parallel to the line $straight x over 2 space equals space straight y over 3 space equals space fraction numerator straight z over denominator negative 6 end fraction$

Some More Questions From Three Dimensional Geometry Chapter

Find the direction cosines of x, y and z-axis.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction