χ { ((x= t+1)),((y= 2t−3)),((z= −t +2)) :} Δ { ((x= 3t +2)),((y= −t−1 )),((z= t+1)) :} { ((Are these two lines located)),((in the same plane or not?)),((where t∈ R)) :}


Question and Answers Forum

All Questions Topic List
Coordinate Geometry Questions
Previous in All Question Next in All Question
Previous in Coordinate Geometry Next in Coordinate Geometry
Question Number 182772 by Acem last updated on 14/Dec/22

$χ {\begin{cases} x = t + 1 \\ y = 2 t - 3 \\ z = - t + 2 \end{cases} Δ {\begin{cases} x = 3 t + 2 \\ y = - t - 1 \\ z = t + 1 \end{cases} {\begin{cases} A r e t h e s e t w o l i n e s l o c a t e d \\ i n t h e s a m e p l a n e o r n o t ? \\ w h e r e t \in R \end{cases}$
	Answered by mr W last updated on 14/Dec/22

	$M e t h o d I$ $l i n e 1 : (1, - 3, 2) + s (1, 2, - 1)$ $l i n e 2 : (2, - 1, 1) + t (3, - 1, 1)$ ${i t}^{'} s t o s e e t h a t b o t h l i n e s a r e n o t$ $p a r a l l e l .$ $a s s u m e t h e y l i e i n t h e s a m e p l a n e,$ $t h e n t h e y s h o u l d i n t e r s e c t .$ $1 + s = 2 + 3 t . . . (i)$ $- 3 + 2 s = - 1 - t . . . (i i)$ $2 - s = 1 + t . . . (i i i)$ $f r o m (i) a n d (i i i) :$ $\Rightarrow t = 0, s = 1$ $p u t t h i s i n t o (i i) :$ $- 3 + 2 = - 1 - 0 ✓$ $t h a t m e a n s b o t h l i n e s i n t e r s e c t i n d e e d .$ $t h e y l i e i n t h e s a m e p l a n e .$
	Commented by mr W last updated on 14/Dec/22

	$M e t h o d I I$ $v e c t o r 1 : (1, 2, - 1)$ $v e c t o r 2 : (3, - 1, 1)$ $v e c t o r 3 : (1, 2, - 1) = \vec{P Q} )$ $n_{1} = v_{1} \times v_{3} = (0, 0, 0)$ $n_{2} = v_{2} \times v_{3} = (- 1, 4, 7)$ $n_{1} / / n_{2} . t h e l i n e s a r e c o p l a n a r .$ $) {i t}^{'} s t o s e e t h a t p o i n t Q o n l i n e 2$ $l i e s a l s o o n l i n e 1, b o t h l i n e s a r e i n$ $t h e s a m e p l a n e .$
	Commented by Acem last updated on 14/Dec/22

	$Y e s S i r! e x a c t l y t h a n k s s s s$ $a n d t h e i n t e r s e c t i o n p o i n t i s C (2, - 1, 1) \in P$ $H a v e a g o o d t i m e$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum