Multiplying a vector v by a scalar k creates a new vector with magnitude kv. If k is positive, the new vector points in the same direction as v, and if k is negative, it points in the opposite direction of v. The document also reviews trigonometry ratios for right triangles, reminding the reader that the Pythagorean theorem can be used as a2 + b2 = c2 and trig functions like sine, cosine, and tangent can help solve for unknown angles or sides.

1. Vectors Lesson 5-3 Multiplying a Vector by a Scalar and Trigonometry Review

2. Multiplying by a Scalar Multiplication can be thought of as a shorthand way to write a repeated addition: 4 + 4 + 4 = 3 x 4 This concept can be used with vectors. 3 v = v + v + v The multiplication of a vector v by a scalar, k, creates a new vector with a magnitude kv. If k is positive, the direction of kv is the same as that of v, if k is negative, the direction of kv is opposite of that of v.

3. Trigonometry Review Right angle triangles: The Pythagorean Theorem a 2 + b 2 = c 2 c a b q Use trig ratios to solve for an angle: sin q = o/h cos q = a/h tan q = o/a h q a o