Vectors

Worked examples (6)

• 1Plane through a point with a given normal
• 2Reading the normal off a Cartesian plane
• 3Plane through three points
• 4Parametric form to Cartesian form
• 5Where a line meets a plane
• 6Cartesian form to parametric form

Model answers (6)

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Worked examples (6)

• 1Magnitude of a cross product from the angle
• 2Testing whether two vectors are parallel
• 3Area of a triangle from three points
• 4Order matters — anti-commutativity
• 5Proving three points are collinear
• 6Area of a parallelogram and a unit normal

Model answers (6)

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Worked examples (6)

• 1Cross products of the basis vectors
• 2A first cross product by determinant
• 3Verify perpendicularity with the dot product
• 4A vector perpendicular to two given vectors
• 5Normal to a plane through three points
• 6Magnitude of a cross product

Model answers (6)

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Worked examples (6)

• 1Vector equation of a line through two points
• 2Is a point on the line?
• 3Angle between two lines
• 4Finding the point of intersection
• 5Classifying lines as skew
• 6Showing two lines are perpendicular

Model answers (6)

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Worked examples (6)

• 1Angle between two lines using the scalar product
• 2Angle between a line and a plane
• 3Angle between two planes
• 4Perpendicular distance from a point to a plane
• 5Foot of perpendicular and reflection of a point in a plane
• 6Line of intersection of two planes

Model answers (6)

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Worked examples (6)

• 1Computing a vector product
• 2Area of a triangle from position vectors
• 3Shortest distance from a point to a line
• 4Shortest distance between two skew lines
• 5Volume of a parallelepiped (scalar triple product)
• 6Skew distance and verifying the lines are skew

Model answers (6)

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• ✓Model answer 6