How can we find out foot of perpendicular and image of a point in plane ?
Gow can we find out equation of plane passing through 2 planes?

Asked by Vishal | 21st Nov, 2017, 10:50: PM

Expert Answer:

begin mathsize 16px style if space equation space of space plane space is
ax plus by plus cz minus straight d equals 0
foot space of space prependicular space left parenthesis straight h comma straight k comma straight l right parenthesis space from space straight a space point space open parentheses straight x subscript 1 comma straight y subscript 1 comma straight z subscript 1 close parentheses space is space given space by
fraction numerator straight h minus straight x subscript 1 over denominator straight a end fraction equals fraction numerator straight k minus straight y subscript 1 over denominator straight b end fraction equals fraction numerator straight l minus straight z subscript 1 over denominator straight c end fraction equals fraction numerator negative open parentheses ax subscript 1 plus by subscript 1 plus cz subscript 1 minus straight d close parentheses over denominator straight a squared plus straight b squared plus straight c squared end fraction
image space of space straight a space point open parentheses straight x subscript 1 comma straight y subscript 1 comma straight z subscript 1 close parentheses space is space given space by
fraction numerator straight h apostrophe minus straight x subscript 1 over denominator straight a end fraction equals fraction numerator straight k apostrophe minus straight y subscript 1 over denominator straight b end fraction equals fraction numerator straight l apostrophe minus straight z subscript 1 over denominator straight c end fraction equals fraction numerator negative 2 open parentheses ax subscript 1 plus by subscript 1 plus cz subscript 1 minus straight d close parentheses over denominator straight a squared plus straight b squared plus straight c squared end fraction
where left parenthesis straight h apostrophe comma straight k apostrophe comma straight l apostrophe right parenthesis space is space the space image
equation space of space plane space passing space through space 2 space planes space is space given space by space family space of space plane
straight P subscript 1 plus λP subscript 2 equals 0
straight P subscript 1 space & space straight P subscript 2 space are space equation space of space planes end style

Answered by Arun | 29th Nov, 2017, 11:31: AM