How do you write a vector equation and a parametric equation for each line: the line through A(-1,2,1) and B(1,2,1)?

Answer 1

Vector equation
#r(lambda)=(-1,2,1)+lambda(2,0,0)#

Parametric equation
#" "##x=-1+2lambda#

r(t) = #y=2#

#" "##z=1#

The vector equation of a line involves a point on the line and the vector direction of the line.

So using point A #(-1,2,1)# and direction #vec(AB)#

we get a line with vector equation

#r(lambda)=A+lambda*vec(AB)#
#r(lambda)=(-1,2,1)+lambda((1,2,1)-(-1,2,1))#
#r(lambda)=(-1,2,1)+lambda(2,0,0)#

To parametrically define this line we now take each component (x,y,z) or (i,j,k) individually

#" "##x=-1+2lambda#
r(t) = #y=2#
#" "##z=1#
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Answer 2

Vector equation: ( \mathbf{r} = \mathbf{a} + t(\mathbf{b} - \mathbf{a}) )
Parametric equations:
[ x = -1 + t(1 - (-1)) ]
[ y = 2 + t(2 - 2) ]
[ z = 1 + t(1 - 1) ]

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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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