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Finding the unknown cordinates of a point on a vector 
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#1
Dec1812, 09:55 AM

P: 8

Relative to the origin O, the position vectors of two points A and B are (1,4) and (7,1) respectively. Give that the point P (t,t+1) is on AB find
1) AP and BP in terms of t 2) Find the value of t and hence the ratio AP:PB Solution: 1) AP= (i  4 j) + ti + (t+1)J = (t1)i + (t3)j BP= 7i j + ti + (t+1)j =(t7)i + (t)j 2) I have no idea how to find t. 


#2
Dec1812, 10:43 AM

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#3
Dec1812, 11:02 AM

P: 8

0 = AP X PB 0= ((t 1)i + (t3)j) X (( T7)i + tj) 0 =  (t3)(t7)k + (t1)t k 0 = (3t)(t7) k + (t1)tk 0= (3t t^221+7t)k + (t1)tk 0= (10t t^2 21)k + (t1)tk 0= (10t t^2 21)k +(t^2  t)k 0= (9t 21)k 9t21=0 9t=21 t= 7/3 


#4
Dec1812, 11:07 AM

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Finding the unknown cordinates of a point on a vector



#5
Dec1812, 11:20 AM

P: 8

Wouldn't that just introduce another unknown variable which would require us to have 2 equations in order to solve. I thought this route already but didn't bother going this way since I don't know the ratio, and hence the value of k. 


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Dec1812, 11:31 AM

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#7
Dec1812, 11:33 AM

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