The distance of the point `(1,3,-7)`from the plane passing through the point `(1,-1,-1),`having normal perpendicular to both the lines`(x-1)/1=(y+2)/(-2)=(z-4)/3a n d(x-2)/2=(y+1)/(-1)=(z+7)/(-1)i s:``5/(sqrt(83))`(2) `(10)/(sqrt(74))`(3) `(20)/(sqrt(74))`(4) `(10)/(sqrt(83))`A. `(20)/(sqrt(74))`unitsB. `(10)/(sqrt(83))` unitsC. `(5)/(sqrt(83))`unitsD. `(10)/(sqrt(74))`units

The distance of the point `(1,3,-7)`from the plane passing through the

1.	The distance of the point `(1,3,-7)`from the plane passing through the point `(1,-1,-1),`having normal perpendicular to both the lines`(x-1)/1=(y+2)/(-2)=(z-4)/3a n d(x-2)/2=(y+1)/(-1)=(z+7)/(-1)i s:``5/(sqrt(83))`(2) `(10)/(sqrt(74))`(3) `(20)/(sqrt(74))`(4) `(10)/(sqrt(83))`A. `(20)/(sqrt(74))`unitsB. `(10)/(sqrt(83))` unitsC. `(5)/(sqrt(83))`unitsD. `(10)/(sqrt(74))`units
Answer» Correct Answer - B Given, equations of lines are `(x-1)/(1)=(y+2)/(-2)=(z-4)/(3)` and`" "(x-2)/(2)=(y+1)/(-1)=(z+7)/(-1)` Let `n_(1)=hati-2hatj+3hatk` and `n_(2)=2hati-hatj-hatk` `:.` Any vector n perpendicular to both `n_(1),n_(2)` is given by `n=n_(1)xxn_(2)` `implies" "n=\|{:(hati,hatj,hatk),(1,-2,3),(2,-1,-2):}\|=5hati+7hatj+3hatk` `:.` Eauation of a plane passing through (1,-1,-1) and perpendicular to n is given by `5(x-1)+7(y+1)+3(z+1)=0` `implies" "5x+7y+3z+5=0` `:.` Required distance`=\|(5+21-21+5)/(sqrt(5^(2)+7^(2)+3^(2)))\|=(10)/(sqrt(83))` units

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