Consider the vector 𝑣⎯⎯⎯ v ¯ between (−2,4,−5) ( − 2 , 4 , − 5 ) and (5,−2,−4) ( 5 , − 2 , − 4 ) .

Question

1. the vector v ¯ is?
2. THE LENGTH OF v ¯ IS?
3. if the tail of v ¯ is at (5,-1,1), then the tip is at?
4. if the tip of v ¯ is at (0, -5, -2) then the tail is at ?
5. what vector has the same length as v ¯ but points in the opposite direction?
6. What vector has the same direction as v ¯ but twice as long?

Answer 1

(1) The vector v is simply

v = <x₂ - x₁, y₂ - y₁, z₂ - z₁>

v = <5 - (-2), -2 - 4, -4 - (-5)>

v = <7, -6, -9>

(2) The length of v is

|v| = √(7² + (-6)² + (-9)²)

|v| = √(49 + 36 + 81)

|v| = √166

(3) If the tail of v is at (5, -1, 1), then the tip is at (5 + 7, -1 - 6, 1 - 9) = (12, -7, -8).

(4) If the tip of v is at (0, -5, -2), then the tail is at (0 - 7, -5 + 6, -2 + 9) = (-7, 1, 7).

(5) The vector with the same length as v but pointed in the opposite direction is the vector w = -v = <-7, 6, 9>.

(6) The vector with the same direction as v but double the length is the vector w = 2v = <14, -12, -18>.