Consider the line which passes through the point P(1, 5, 4), and which is parallel to the line x=1+5t y=2+5t z=3+5t. How do you find the point of intersection of this new line with each of the coordinate planes?
The reqd. pts. of intersection are,
We note that the Direction Vector of the given line is,
let us recall that, their resp. eqns. are,
Thus, the reqd. pts. of intersection are,
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To find the point of intersection of the line passing through point P(1, 5, 4) and parallel to the line (x=1+5t), (y=2+5t), (z=3+5t) with each of the coordinate planes, follow these steps:

Intersection with the xyplane (z = 0): Substitute (z = 0) into the equation of the line to find the corresponding (x) and (y) coordinates. Then solve for (t). [ 4 + 5t = 0 \Rightarrow t = \frac{4}{5} ] Substitute (t = \frac{4}{5}) into the equations of the line to find (x) and (y).

Intersection with the xzplane (y = 0): Substitute (y = 0) into the equation of the line to find the corresponding (x) and (z) coordinates. Then solve for (t). [ 5 + 5t = 0 \Rightarrow t = 1 ] Substitute (t = 1) into the equations of the line to find (x) and (z).

Intersection with the yzplane (x = 0): Substitute (x = 0) into the equation of the line to find the corresponding (y) and (z) coordinates. Then solve for (t). [ 1 + 5t = 0 \Rightarrow t = \frac{1}{5} ] Substitute (t = \frac{1}{5}) into the equations of the line to find (y) and (z).
This process yields the points of intersection of the given line with each of the coordinate planes.
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When evaluating a onesided 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 onesided 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 onesided 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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