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How do you write a vector equation and a parametric equation for each line: the line through A(3,0,4) and parallel to the x-axis?

Answer 1

Samantha Adkison

#r=(3. 0, 4)+(x, 0, 0)=(x+3, 0, 4)# x can be regarded as the parameter for the parametric form.

Equation x-axis is# r= (x, 0, 0)#.

So, the equation to the line, parallel to the x-axis through (a, b, c) is

#r=(a, b, c)+(x, 0, 0)#.

Here, it is #r=(3, 0. 4)+(x, 0, 0)=(3+x, 0, 4)#.

This is itself in parametric form, with x as the parameter. Note that y

and z are constants on this line.

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Answer 2

Aurora Alvarado

Vector equation: r = (3 + at) i + 0 j + (4 + bt) k Parametric equations: x = 3 + at, y = 0, z = 4 + bt

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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.