# Find the equations of the lines through the following pairs of points inspace. (a) (3, −2,4) and (-5,7,1)  (b) (2,4,0) and (−3, −6,0)  (c) (3,7,2) and (3,7, −8) (d) (−2, −1,5) and (3,9,7)

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Find the equations of the lines through the following pairs of points inspace. (a) (3, −2,4) and (-5,7,1)  (b) (2,4,0) and (−3, −6,0)  (c) (3,7,2) and (3,7, −8) (d) (−2, −1,5) and (3,9,7)

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Step 1

(a)

Consider the given points: (a1,a2,a3)=(3, −2,4) and (b1,b2,b3) = (-5,7,1)

Now, find vector between them:

v= <v1,v2,v3> = <3-(-5),-2-7,4-1>

= <8,-9,3>

Now, the required equation of line through the given points will be given by:

Step 2

(b)

Consider the given points: (a1,a2,a3)= (2,4,0) and (b1,b2,b3) = (−3, −6,0)

Now, find vector between them:

v= <v1,v2,v3> = <2-(-3),4-(-6),0-0>

= <5,10,0>

Now, the required equation of line through the given points will be given by:

Step 3

(c)

Consider the given points: (a1,a2,a3)= (3,7,2) and (b1,b2,b3) = (3,7, −8)

Now, find vector between them:

v= <v1,v2,v3> = <3-3,7-7,2-(-8)>

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