find the vector equation of the coordinate plane 

Asked by Sandeep Yadav | 10th Dec, 2014, 07:01: AM

Expert Answer:

T h e space v e c t o r space e q u a t i o n space o f space a space p l a n e space p a s sin g space t h r o u g h space a space p o i n t space h a v i n g space p o s i t i o n space v e c t o r space a with rightwards arrow on top space a n d space n o r m a l space t o space v e c t o r space n with rightwards arrow on top space i s open parentheses r with rightwards arrow on top minus a with rightwards arrow on top close parentheses times n with rightwards arrow on top equals 0 C o n s i d e r space t h e space X Y space p l a n e. space A n y space p o i n t space i n space t h e space X Y space p l a n e space i s space o f space t h e space f o r m comma a with rightwards arrow on top equals a subscript 1 i with hat on top plus a subscript 2 j with hat on top T h e space n o r m a l space t o space X Y space p l a n e space i s space z minus a x i s space a n d space i t s space e q u a t i o n space i s space 0 cross times i with hat on top plus 0 cross times j with hat on top plus 1 cross times k with hat on top T h u s comma space e q u a t i o n space o f space X Y space p l a n e space i s open square brackets open parentheses x minus a subscript 1 close parentheses i with hat on top plus open parentheses y minus a subscript 2 close parentheses j with hat on top plus open parentheses z minus 0 close parentheses k with hat on top close square brackets times open square brackets 0 cross times i with hat on top plus 0 cross times j with hat on top plus 1 cross times k with hat on top close square brackets equals 0 rightwards double arrow open parentheses z minus 0 close parentheses k with hat on top times k with hat on top equals 0 S i m i l a r l y comma space C o n s i d e r space t h e space Y Z space p l a n e. space A n y space p o i n t space i n space t h e space Y Z space p l a n e space i s space o f space t h e space f o r m comma a with rightwards arrow on top equals a subscript 2 j with hat on top plus a subscript 3 k with hat on top T h e space n o r m a l space t o Y Z space p l a n e space i s space x minus a x i s space a n d space i t s space e q u a t i o n space i s space 1 cross times i with hat on top plus 0 cross times j with hat on top plus 0 cross times k with hat on top T h u s comma space e q u a t i o n space o f space X Y space p l a n e space i s open square brackets open parentheses x minus 0 close parentheses i with hat on top plus open parentheses y minus a subscript 2 close parentheses j with hat on top plus open parentheses z minus a subscript 3 close parentheses k with hat on top close square brackets times open square brackets 1 cross times i with hat on top plus 0 cross times j with hat on top plus 0 cross times k with hat on top close square brackets equals 0 rightwards double arrow open parentheses x minus 0 close parentheses i with hat on top times i with hat on top equals 0 S i m i l a r l y comma space C o n s i d e r space t h e space X Z space p l a n e. space A n y space p o i n t space i n space t h e space X Z space p l a n e space i s space o f space t h e space f o r m comma a with rightwards arrow on top equals a subscript 1 i with hat on top plus a subscript 3 k with hat on top T h e space n o r m a l space t o X Z space p l a n e space i s space y minus a x i s space a n d space i t s space e q u a t i o n space i s space 0 cross times i with hat on top plus 1 cross times j with hat on top plus 0 cross times k with hat on top T h u s comma space e q u a t i o n space o f space X Z space p l a n e space i s open square brackets open parentheses x minus a subscript 1 close parentheses i with hat on top plus open parentheses y minus 0 close parentheses j with hat on top plus open parentheses z minus a subscript 3 close parentheses k with hat on top close square brackets times open square brackets 0 cross times i with hat on top plus 1 cross times j with hat on top plus 0 cross times k with hat on top close square brackets equals 0 rightwards double arrow open parentheses y minus 0 close parentheses j with hat on top times j with hat on top equals 0

Answered by Vimala Ramamurthy | 10th Dec, 2014, 12:09: PM