Application of DerivativeHard
Question
The d.r. of normal to the plane through (1, 0, 0) , (0, 1, 0) which makes an angle π/4 with plane x + y = 3 are
Options
A.1, √2, 1
B.1, 1, √2
C.1, 1, 2
D.√2, 1, 1
Solution
Equation of plane through (1, 0, 0) is
a(x - 1) + by + cz = 0 ........ (i)
(i) passes through (0, 1, 0)
- a + b = 0 ⇒ b = a; Also, cos 45o =
⇒ 2a =
⇒ 2a2 = c2 ⇒ c = √2a
So. d.r. of normal are a, a √2a i.e. 1,1,√2
a(x - 1) + by + cz = 0 ........ (i)
(i) passes through (0, 1, 0)
- a + b = 0 ⇒ b = a; Also, cos 45o =
⇒ 2a =
⇒ 2a2 = c2 ⇒ c = √2aSo. d.r. of normal are a, a √2a i.e. 1,1,√2
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