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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x

y

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

w

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)