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# consider the Line L is given by L: r(t) = <3t +1, t+2, 2t-1>and two planes P1 and P2 given by P1 :

x+y-z = 6, P2 :2x-2y + 2z =2

a)Does the line L intersect the Plane P1? If so , find the point of intersection. If not explain

b)Find the angle between P1 and P2. leave answer as sarcosine of some number

c)Find the distance between origin and line L

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Given equation of line: &lt; 3t+1, + +2 ,2t-17
Writing it in standat form , I get
2
y
a New plane P,: ity- 2= 6
Investing the cartesian form of the equation,
get joy
( 3 + + 1 ) + ( + + 2 ) -... Mtyaz = 6
Waiting the plane P, in the standard form
37. D = C, we get.
( ~ ] + y ]+ 3k ). ( 2 +g -k ) = 6
= uti - k
P ,:
2n- Ly +23 = 2
=) u- y +3 = 2 . Writing at in form s. W= C.
[ n s + y 3 + 3 k ] . [ x - J + *] = 2.
M2= 1 - 1+k
Angle b/w the two planes , O
=)
inil . In21
= ) [ x - J + f ] . [ x + J - R ]
9
us Q . = )
3
(0) LineL: &lt; 3+ +1, +... ### Why Join Course Hero?

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