1. Find the vector v with the given magnitude and the same direction as u.
Magnitude: v = 7
Direction: u = <−8, 8, 2>
v=?
2.Use the vectors to find the point that lies two-thirds of the way from P to Q.
P(1, 2, 5)
Q(6, 8, 4)
(x,y,z) = ?
Calculus III - Vectors Help?
2015-09-03 2:14 pm
回答 (1)
2015-09-03 3:55 pm
✔ 最佳答案
1.v
= 7 ( unit vector of u )
= ｜v｜( u /｜u｜)
= 7 < - 8 , 8 , 2 > / √ [ (-8)^2 + 8^2 + 2^2 ]
= 7 < - 8 , 8 , 2 > / √132
= 7 < - 8 , 8 , 2 > / 2√33
= < - 28/√33 , 28/√33 , 7/√33 > ... Ans
2.
Suppose the point that lies two-thirds of the way from P to Q is R(x,y,z)
So, PR = (2/3) PQ
( x-1 , y-2 , z-5 ) = (2/3) ( 5 , 6 , -1 ) = ( 10/3 , 4 , - 2/3 )
(x,y,z) = ( 1+10/3 , 2+4 , 5-2/3 ) = ( 13/3 , 6 , 13/3 )
Ans: ( 13/3 , 6 , 13/3 )
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