Question:
The position vectors of three points A, B and C are ab , and c , respectively, such that 34 0ab c . What is AB : BC equal to?
The position vectors of three points A, B and C are ab , and c , respectively, such that 34 0ab c . What is AB : BC equal to?
Options:
- a) 3 : 1
- b) 1 : 3
- c) 3 : 4
- d) 1 : 4
- a) 3 : 1
- b) 1 : 3
- c) 3 : 4
- d) 1 : 4
correct answer : b)
Explanation:
34 0ab c
-+ =
Þ 33ab bc
— + = 0
Þ 3( )ab
– = bc
– Þ 3( )ba
– = cb
–
Þ ba
cb
-
–
= 1
3
Þ AB
BC
/combarrowextender/arrowrightnosp/combarrowextender/combarrowextender
/combarrowextender/arrowrightnosp/combarrowextender/combarrowextender
= 1
3
34 0ab c
-+ =
Þ 33ab bc
— + = 0
Þ 3( )ab
– = bc
– Þ 3( )ba
– = cb
–
Þ ba
cb
-
–
= 1
3
Þ AB
BC
/combarrowextender/arrowrightnosp/combarrowextender/combarrowextender
/combarrowextender/arrowrightnosp/combarrowextender/combarrowextender
= 1
3