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If the points `(1," "1," "p)" "a n d" "(" "3," "0," "1)`be equidistant from the plane ` -> rdot(3 hat i+4 hat j-12 hat k)+13=0`, then find the value ofp. |
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Answer» Distance between the point and the plane is given by, `l_(1)=|{:(veca*vecn-d)/(|n|):}|` ...(i) `veca=hat("i")+hat(j)+hat(k)`, `vecn=3hat("i")+4hat(j)-12hat(k)` `veca*vec(n)=3+4-12=-5` `vecd=-13` From (i) , `=|(-5+13)/(sqrt(9+16+144))|=(8)/(13)` Again, `veca=-3hat("i")+0hat(j)+hat(k)` Them , `l_(2)=|((3hat("i")+0hat(j)+hat(k))*(3hat("i")+4hat(j)-12hat(k))+13)/(sqrt(9+16+144))|` `=|(-9-12+13)/(13)|` `=(8)/(13)` `thereforel_(1)=l_(2)` |
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