Vectors in the Coordinate Plane: Component Form and Magnitude

What is the component form of vector 𝑣 with an initial point 𝑃(0, −7) and a terminal point 𝑄(−9,0)?

What is the result of 2𝐮 − 𝐯, expressed as a linear combination of vectors i and j, given 𝐮 = 〈−10,4〉 and 𝐯 = 〈2,3〉?

What is the unit vector with the same direction as 𝐯 = 〈−4, −3〉?

What is the dot product of vectors 𝑢 =< 5,3 > and 𝑣 =< 12,4 >?

For two vectors to be orthogonal, the dot product must equal to __________________.

What is the component form and magnitude of vector 𝑃𝑄?

What are the components of the vector 2𝑢 + 3𝑤?

Find a unit vector in the direction of the vector 𝑤 = 5𝑖 + 5𝑗.

What is the magnitude and direction angle of the vector −3𝑖 − 5𝑗?

Given 𝐫 = 5𝐢 − 𝐣, what is the magnitude of 𝐫?