Objective: Projection of vector onto another. Orthogonal vectors.

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Objective: Projection of vector onto another. Orthogonal vectors. Warm up Find the angle between the two vectors: The angle between vectors v and w is . Find . Orthogonal (vectors): Vectors v and w are orthogonal iff .

Example 1 Determine whether v and w are orthogonal. a. b.

Projection of a vector onto another. Pushing boat down the ramp Pressing the boat against ramp (due to gravity) pulling straight down A method of finding and involves projecting a vector onto another.

Projection of v onto w: v w

Example 2 Find the vector projection of onto . Write v as the sum of two orthogonal vectors.

Example 3 Let and . Find . Write v as the sum of two orthogonal vectors.