# How do you find the parametric equations for the line through the point (2,3,4) and perpendicular to the plane 3x + 2y -Z = 6?

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To find the parametric equations for the line through the point (2,3,4) and perpendicular to the plane 3x + 2y - z = 6, follow these steps:

- Determine the direction vector of the line.
- Use the normal vector of the plane to find the direction vector of the line.
- Write the parametric equations using the given point and direction vector.

Step 1: Determine the direction vector of the line. Let's call the direction vector of the line ( \vec{d} = (a, b, c) ).

Step 2: Use the normal vector of the plane to find the direction vector of the line. The normal vector of the plane is ( \vec{n} = (3, 2, -1) ). Since the line is perpendicular to the plane, the direction vector of the line is parallel to the normal vector of the plane. Hence, ( \vec{d} ) is proportional to ( \vec{n} ). So, ( \vec{d} = k \vec{n} ), where ( k ) is a scalar.

Step 3: Write the parametric equations using the given point and direction vector. The parametric equations of the line passing through the point ( (x_0, y_0, z_0) ) with direction vector ( \vec{d} = (a, b, c) ) are: [ x = x_0 + at ] [ y = y_0 + bt ] [ z = z_0 + ct ]

Given point: ( (2, 3, 4) )

So, substituting the values: [ x = 2 + 3kt ] [ y = 3 + 2kt ] [ z = 4 - kt ]

These are the parametric equations for the line passing through the point (2,3,4) and perpendicular to the plane 3x + 2y - z = 6.

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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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