Equation of Tangent at a Point (x,y) in Terms of f'(x)
If a line whi...
Question
If a line which passes through the point A(0,1,2) and makes angle π4,π4,π2 with x,y,&z axes respectively. The line meets the plane x+y+z=0 at point B. The length √2AB is equal to
A
3
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B
−3
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C
4
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D
3√2
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Solution
The correct option is A3 The D.C. of the line are (1√2,1√2,0) any point on the line at a distance λ from A(0,1,2) is (0+λ√2,1+λ√2,2+λ.0) which lies on x+y+z=0 ∴λ√2+(1+λ√2)+2=0 ⇒2λ√2=−3⇒λ=−3√2 ∴B=(−32,−12,2) A=(0,1,2)&B≡(−32,−12,2) AB=√94+94=3√22=3√2