Consider the plane (x,y,z)=(0,1,1)+λ(1,−1,1)+μ(2,−1,0). The distance of this plane from the origin is:
A
13
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B
√32
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C
√32
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D
2√3
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Solution
The correct option is B√32 Given (x,y,z)=(0,1,1)+λ(1,−1,1)+μ(2,−1,0) ⇒xi+yj+zk=j+k+λ(i−j+k)+μ(2i−j) Comparing coefficients of i,j and k, λ+2μ=x..(1) −λ−μ=y−1..(2) −2μ=y+z−2..(3) Eliminating λ and μ from (1), (2) and (3), we get x+2y+z+3=0 Hence, distance of this plane from origin is =∣∣
∣∣3√12+22+12∣∣
∣∣=√32