Quiz on Vector Addition

Which law of vector addition is illustrated by the equation a + b = b + a?

• Distributive Law

• Associative Law

• Commutative Law

• Identity Law

What is the purpose of shifting vector $ -b $ in vector subtraction?

• To align it with vector $ a $

• To make it parallel to vector $ a $

• To ensure its head touches the tail of $ a $

• To reverse its direction

Which of the following is NOT a property of the zero vector?

• 0 × u = 0

• u × 0 = 0

• u + 0 = 0

• u - 0 = u

What is the result of simplifying the expression \(3a + b - 6(a + 3b)\)?

• \(-3a - 17b\)

• \(3a + 17b\)

• \(-3a + 17b\)

• \(3a - 17b\)

In the expression \(3a + b - 6(a + 3b)\), what is the coefficient of \(b\) after simplification?

• \(-17\)

• \(17\)

• \(-6\)

• \(6\)

What is the simplified form of the expression \(3(a - 5b)\)?

• \(3a - 15b\)

• \(3a + 15b\)

• \(3a - 5b\)

• \(3a + 5b\)

What is the commutative law for vector addition?

• a + b = b + a

• a + 0 = a

• m(a + b) = ma + mb

• a + (-a) = 0

If a is parallel to b, what condition must be satisfied?

• a = b

• a = kb for some k

• a + b = 0

• a - b = 0

How can \( \overrightarrow{CD} \) be expressed in terms of vectors \( \overrightarrow{v} \) and \( \overrightarrow{w} \)?

• \( \overrightarrow{v} \)

• \( \overrightarrow{w} \)

• \( \overrightarrow{v} + \overrightarrow{w} \)

• \( \overrightarrow{v} - \overrightarrow{w} \)