Extended Work on 3D Lines and Planes. Intersection of a Line and a Plane Find the point of intersection between the line and the plane Answer: (2, -3,

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Presentation transcript:

Extended Work on 3D Lines and Planes

Intersection of a Line and a Plane Find the point of intersection between the line and the plane Answer: (2, -3, 2) Find the point of intersection between the line and the plane Answer: (1, 3, 7)

Let P be the point (1, 0, -2) and be the plane Let P` be the reflection of P in the plane. Find the coordinates of the point P`. Answer:

Distance of a Point to a Plane 1. Find the equation of the line which passes through the point and is perpendicular to the plane. 2. Find the point of intersection of the line and the plane. 3. Find the distance from the point and the point of intersection. Find the distance from the point (3, -2, 6) to the plane Answer:

Find the distance from the point (1, 5, -4) to the plane Answer: Find the distance from the point (2, 8, 4) to the plane

Answer: Find the distance between the two parallel planes given by Answer: Find the distance between the two parallel planes given by

Distance Between a Point and a Line 1. Find the vector from Q to the line at R. 2. This vector must be perpendicular to the vector u. 3. Solve the scalar product for the scalar. 4. Find the point of intersection R. 5. Find the distance from Q to R.

Find the distance between the point Q(3, -1, 4) and the line given by Answer: Find the distance between the point Q(1, 5, -2) and the line given by Answer:

Find the distance between the two skew lines below Answer: and Find the distance between the two skew lines below and

The line and the plane intersect at the point P. Find the coordinates of P. Answer: M04/HL1/10/TZ1 Show that the line lies in the plane

a) Find the Cartesian equation of the plane that contains the origin O and the points A(1, 1, 1) and B(2, -1, 3). b) Find the distance from the point C(10, 5, 1) to the plane OAB. Answer: N04/HL1/19

Angle Between a Line and a Plane 1. Use the normal vector for the plane and the direction vector for the line. 2. Find the angle between these two vectors. 3. Make sure that this angle is the acute angle between these two vectors. 4. These two vectors will form a triangle. So, subtract this angle and the right angle from the triangle to find the angle between the line and the plane.

Find the angle between the plane below and the z-axis. Give your answer to the nearest degree. Answer: 48 degrees N03/HL1/7 Find the angle between the line and the plane below. Answer: 0.100

Find the angle between the line and the plane below. Answer: Find the angle between the line and the plane below. Answer: 1.15