Questions: Vector v has components of ⟨5,8⟩. Vector w is equivalent to 4 v. What are the components of vector w? <5,8> <-5,-8> <20,16> <20, 32> <40, 64>

Solution Steps

The vector \( v \) has components \( \langle 5, 8 \rangle \).

Vector \( w \) is equivalent to \( 4v \), which means it is \( 4 \) times vector \( v \).

Multiply each component of vector \( v \) by \( 4 \): \[ w = 4v = 4 \cdot \langle 5, 8 \rangle = \langle 4 \cdot 5, 4 \cdot 8 \rangle = \langle 20, 32 \rangle \]

Final Answer