Ncert Solutions Maths class 12th
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Let a plane P contain two lines r = î + λ(î + ĵ), λ ∈ R and r = −ĵ + μ(ĵ − k̂), μ ∈ R. If Q(α, β, γ) is the foot of the perpendicular drawn from the point M(1,0,1) to P, then 3(α + β + γ) equals
Let a plane P contain two lines r = î + λ(î + ĵ), λ ∈ R and r = −ĵ + μ(ĵ − k̂), μ ∈ R. If Q(α, β, γ) is the foot of the perpendicular drawn from the point M(1,0,1) to P, then 3(α + β + γ) equals
Normal of plane = |î? k|
|1 0|
|0 1 -1|
n = -î+? +k
D.R.'s = -1,1,1
Plane => -1 (x-1)+1 (y-0)+1 (z-0) = 0
=> x-y-z-1=0
If (x, y, z) is foot of perpendicular of M (1,0,1) on the plane then
(x-1)/-1 = (y-0)/1 = (z-1)/1 = - (1-0-1-1)/3
x=4/3, y=-1/3, z=2/3
α+β+γ = 4/3 - 1/3 + 2/3 = 5/3
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Suppose f(x) is a polynomial of degree four, having critical points at -1,0,1. If T = {x ∈ R | f(x) = f(0)}, then the sum of squares of all the elements of T is:
Suppose f(x) is a polynomial of degree four, having critical points at -1,0,1. If T = {x ∈ R | f(x) = f(0)}, then the sum of squares of all the elements of T is:
f' (x) = k*x (x+1) (x-1) = k (x³-x)
=> f (x) = k (x? /4 - x²/2) + C
=> f (0) = C
=> f (x) = f (0)
=> k (x? -2x²)/4 + C = C
=> x² (x²-2)=0
=> x = {0, √2, -√2}
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