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if vector v has an initial point at (2,3) and a terminal point at (6,6) and vector w has an initial point at (3,2) and a terminal point at (6,6), are the two vectors equivalent?​

User Carneiro
by
7.5k points

1 Answer

4 votes

Not equivalent

Explanation:

For any two vectors
v_(1) and v
_(2) to be equivalent,

their length and direction has the same.

Distance between two points
(x_(1),y_(1)) and
(x_(2),y_(2))

is
\sqrt{(y_(2)-y_(1))^2+(x_(2)-x_(1))^(2)}

Length of
v_(1) is
\sqrt{(6-3)^(2)+(6-2)^(2)}=√(9+16)=√(25)=5

Length of
v_(2) is
\sqrt{(6-2)^(2)+(6-3)^(2)}=√(16+9)=√(25)=5

Slope of vector
v joining
(x_(1),y_(1)) and
(x_(2),y_(2)) is
(y_(2)-y_(1))/(x_(2)-x_(1))

slope of
v_(1) =
(6-3)/(6-2) =(3)/(4)

slope of
v_(2) =
(6-2)/(6-3) =(4)/(3)

since slope of
v_(1) is not equal to slope of
v_(2),the vectors are not equivalent.

User Camilomq
by
8.1k points

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