Question

If the plane passing through the points (1, 2, 3), (2, 3, 1) and (3, 1, 2) is ax + by + cz = d then a + 2b + 3c = ______.

पर्याय

• 0

• 1

• 6

• 18

Answer 1

If the plane passing through the points (1, 2, 3), (2, 3, 1) and (3, 1, 2) is ax + by + cz = d then a + 2b + 3c = 6.

Explanation:

Equation of plane passing through (1, 2, 3), (2, 3, 1) and (3, 1, 2) is

`|(x - 1,"y" - 2, "z" - 3),(2 - 1, 3 - 2, 1 - 3),(3 - 1, 1 - 2, 2 - 3)|` = 0

`=> |(x - 1, "y" - 2, "z" - 3),(1,1,-2),(2,-1,-1)|` = 0

⇒ (x - 1)(- 3) - (y - 2)(3) + (z - 3)(- 3) = 0

⇒ - 3x + 3 - 3y + 6 - 3z + 9 = 0

⇒ x + y + z = 6

Comparing the above equation with

ax + by + cz = d, we get

a = 1, b = 1, c = 1

Now, , a + 2b + 3c = (1) + 2(1) + 3(1) = 6