Question

how do you combine vectors if they are in opposite directions? use trigonometry add pythagorean theorem subtract

Explanation:

Step1: Understand vector combination rules

Vectors in opposite directions are combined by subtracting their magnitudes. For example, if vector \( \vec{A} \) has magnitude \( A \) in one direction and vector \( \vec{B} \) has magnitude \( B \) in the opposite direction, the resultant vector \( \vec{R} \) has magnitude \( |A - B| \) and direction of the larger - magnitude vector.

Step2: Analyze each option

• Use trigonometry: Trigonometry is used for non - collinear vectors (vectors not in the same or opposite straight line), not for collinear (same or opposite direction) vectors.
• Add: Adding is for vectors in the same direction. If vectors are in the same direction, \( \vec{R}=\vec{A}+\vec{B} \) (magnitude \( R = A + B \)).
• Pythagorean Theorem: The Pythagorean theorem (\( c=\sqrt{a^{2}+b^{2}} \)) is used for perpendicular vectors (\( \vec{A}\perp\vec{B} \)), not for collinear vectors.
• Subtract: As per the rule for collinear vectors in opposite directions, we subtract their magnitudes.

Answer:

Subtract