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?

Answer 1

#vec r(t) = ((2),(3),(4))+t((3),(2),(-1))#

the vector that is normal to that plane is #((3),(2),(-1))#
so #vec r(t) = ((2),(3),(4))+t((3),(2),(-1))#
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Answer 2

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:

  1. Determine the direction vector of the line.
  2. Use the normal vector of the plane to find the direction vector of the line.
  3. 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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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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