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DOT PRODUCT OF VECTORS Mr. Velazquez
Honors Precalculus
THE DOT PRODUCT
THE DOT PRODUCT
THE DOT PRODUCT
ANGLE BETWEEN TWO VECTORS
EXTRA CREDIT: Prove the formula above using Law of Cosines (see diagram, left), and the definition of the magnitude of a vector.
ANGLE BETWEEN TWO VECTORS
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Find the angle 𝜃 between the two vectors Ԧ𝑣 = 2 Ƹ𝑖 − 2 Ƹ𝑗and 𝑢 = −3 Ƹ𝑖 + 5 Ƹ𝑗
PARALLEL AND ORTHOGONAL VECTORS
PARALLEL AND ORTHOGONAL VECTORS
PROJECTION OF A VECTOR ONTO ANOTHER
You know how to add two vectors to obtain a resultant vector. We now reverse this process by expressing a vector as the sum of two orthogonal vectors. By doing this, you can determine how much force is applied in a particular direction.
In the example to the left, we imagine that the force of gravity 𝐹 is the resultant of two orthogonal forces 𝐹1(which pulls the boat down the ramp) and 𝐹2 (which keeps the boat pressed against the ramp).
PROJECTION OF A VECTOR ONTO ANOTHER
PROJECTION OF A VECTOR ONTO ANOTHER
PROJECTION OF A VECTOR ONTO ANOTHER
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If 𝑤 = 6 Ƹ𝑖 + 3 Ƹ𝑗 and Ԧ𝑣 = 2 Ƹ𝑖 + 5 Ƹ𝑗, find the projection of 𝑣 onto 𝑤, and give both vector components of 𝑣.
HOMEWORK: VECTOR DOT PRODUCT
CLASSWORK: VECTOR DOT PRODUCT - Pg. 719, 9-16 (8 questions)
HOMEWORK: Trigonometry HW 7 (Math XL)