A vector has both magnitude and direction. Reverse a route by changing its sign.
Use a consistent direction and match corresponding components.
A scalar multiple proves parallel directions. Collinearity also needs a shared point.
Example 1
and . P lies on the line AB with . Express in terms of a, and .
Subtract the starting position vector from the ending position vector. is the fraction of the whole directed vector .Use the route O → A → P.Collect the a- and -components.
0 < < 1 places P between A and ; > 1 places P beyond B; < 0 places P beyond A.
Example 2
and . P lies on the line AB with . Express in terms of a, and .
Subtract the starting position vector from the ending position vector. is the fraction of the whole directed vector BA.Use the route O → B → P.Collect the a- and -components.
0 < < 1 places P between A and ; > 1 places P beyond A; < 0 places P beyond B.
Your turn
Question 1
and . P lies on the line AB with . Express in terms of a, and .
Check answer
Subtract the starting position vector from the ending position vector. is the fraction of the whole directed vector .Use the route O → A → P.Collect the a- and -components.
0 < < 1 places P between A and ; > 1 places P beyond B; < 0 places P beyond A.
Question 2
and . P lies on the line AB with . Express in terms of a, and .
Check answer
Subtract the starting position vector from the ending position vector. is the fraction of the whole directed vector .Use the route O → A → P.Collect the a- and -components.
0 < < 1 places P between A and ; > 1 places P beyond B; < 0 places P beyond A.
Question 3
and . P lies on the line AB with . Express in terms of a, and .
Check answer
Subtract the starting position vector from the ending position vector. is the fraction of the whole directed vector BA.Use the route O → B → P.Collect the a- and -components.
0 < < 1 places P between A and ; > 1 places P beyond A; < 0 places P beyond B.
Question 4
and . P lies on the line AB with . Express in terms of a, and .
Check answer
Subtract the starting position vector from the ending position vector. is the fraction of the whole directed vector .Use the route O → A → P.Collect the a- and -components.
0 < < 1 places P between A and ; > 1 places P beyond B; < 0 places P beyond A.
Question 5
and . P lies on the line AB with . Express in terms of a, and .
Check answer
Subtract the starting position vector from the ending position vector. is the fraction of the whole directed vector BA.Use the route O → B → P.Collect the a- and -components.
0 < < 1 places P between A and ; > 1 places P beyond A; < 0 places P beyond B.
and . P lies on the line AB with . Express in terms of a, and .
Answer
Subtract the starting position vector from the ending position vector. is the fraction of the whole directed vector .Use the route O → A → P.Collect the a- and -components.
0 < < 1 places P between A and ; > 1 places P beyond B; < 0 places P beyond A.
and . P lies on the line AB with . Express in terms of a, and .
Answer
Subtract the starting position vector from the ending position vector. is the fraction of the whole directed vector .Use the route O → A → P.Collect the a- and -components.
0 < < 1 places P between A and ; > 1 places P beyond B; < 0 places P beyond A.
and . P lies on the line AB with . Express in terms of a, and .
Answer
Subtract the starting position vector from the ending position vector. is the fraction of the whole directed vector BA.Use the route O → B → P.Collect the a- and -components.
0 < < 1 places P between A and ; > 1 places P beyond A; < 0 places P beyond B.
and . P lies on the line AB with . Express in terms of a, and .
Answer
Subtract the starting position vector from the ending position vector. is the fraction of the whole directed vector .Use the route O → A → P.Collect the a- and -components.
0 < < 1 places P between A and ; > 1 places P beyond B; < 0 places P beyond A.
and . P lies on the line AB with . Express in terms of a, and .
Answer
Subtract the starting position vector from the ending position vector. is the fraction of the whole directed vector BA.Use the route O → B → P.Collect the a- and -components.
0 < < 1 places P between A and ; > 1 places P beyond A; < 0 places P beyond B.