Dot Product and Angle Between Two Vectors

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Presentation transcript:

Dot Product and Angle Between Two Vectors

Given two vectors . These vectors are perpendicular if the lines that contain the vectors have a slope whose product is -1. Two vectors are parallel if the lines that contain them are parallel, or, we say that two vectors are parallel if for some real number k.

The Dot Product or Scalar Product If then the dot product of these vectors is defined by: Example: If find:

Properties of the Dot Product Perpendicular vectors are sometimes called orthogonal vectors.

From the Cosine Rule:

The Angle Between Two Vectors

If , and show that and are perpendicular and also show that and are parallel.

If and find . Solution: 4 If and find the measure of the angle between and . Solution: 0.644

If and find the measure of the angle between and . Solution: 1.85 If the angle between the vectors and is 45 degrees, find the two possible values of a. Solution: -4 or 1

The points A, B, C and D have position vectors 5i + j, -3i + 2j, -3i – 3j and i – 6j. Show that is perpendicular to . The points A, B, C and D have position vectors and respectively where , , and . If AC is perpendicular to BD, find the value of y. Solution: 1

Given two non-zero vectors a and b such that find the value of Solution: 0 N02/HL1/14