What is parametric equation of the line created by the intersecting planes x = 2 and z = 2?

Answer 1

#vec r = ((2),(0),(2)) + lambda ((0),(1),(0))#

no need to do much here because every point on the line of intersection will have values x = 2 and z = 2, and any value of y is possible.

a fixed point on the line is (2,0,2) so we can say that the line is this....

#vec r(lambda) = ((2),(0),(2)) + lambda ((0),(1),(0))#
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Answer 2

#vecr=(2,0,2)+t(0,1,0), t in RR#, or,

in the usual Cartesian Form # (x-2)/0=y/1=(z-2)/0#.

Let the given planes be #pi_1 : x-2=0, and pi_2 : z-2=0#.
Let the reqd. line be #L=pi_1 nn pi_2#.
To determine the eqn. of #L#, we need, #(1)# a pt., say, #A in L#, &
#(2)# the direction #vecl# of #L#.

(1) : The point A :-.

#A(x,y,z) in L=pi_1nnpi_2rArr A in pi_1, and, A in pi_2#
#rArr x=2, z=2#. As regards, #y in RR#, y is arbitrary, and, by our
choice, #y=0#. Hence, #A=A(2,0,2)#
(2) : The Direction #vecl# of #L# :-
Let #vecn_1, &, vecn_2# be the normals to #pi_1, &, pi_2#, resp.
#:. vecn_1=(1,0,0)=hati, &, vecn_2=(0,0,1)=hatk#
#L=pi_1nnpi_2 rArr L sub pi_1, &, L sub pi_2 rArr vecl bot vecn_1, &, vecl bot vecn_2#.
#rArr vecl# is along #vecn_1xxvecn_2=hatixxhatk=-hatj=(0,-1,0)#.
we take, #vecl=hatj=(0,1,0)#
Using #(1), &, (2)#, the vector eqn., or, parametric eqn. of #L :#
#vecr=veca+tvecl, t in RR#, where, #veca# is the position vector of
the pt.#A#.
Hence, # L : vecr=(2,0,2)+t(0,1,0), t in RR#, or, in the usual
Cartesian Form # L : (x-2)/0=y/1=(z-2)/0#.

Hope, this will be helpful! Enjoy Maths!

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Answer 3

The parametric equations of the line formed by the intersection of the planes (x = 2) and (z = 2) can be expressed as:

[ \begin{cases} x = 2 \ y = t \ z = 2 \end{cases} ]

Here, ( t ) represents a parameter that can take any real value, which allows us to trace out all points along the line of intersection.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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