DOT PRODUCT OF VECTORS Mr. Velazquez Honors Precalculus
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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v
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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)