Find a nonzero vector u with initial point P(-1.3.-5) such that

[dola]

Find a nonzero vector u with initial point P(-1.3.-5) such that
(a) u has the same direction as v = (6,7,-3)
(b) u is oppositely directed to v = (6,7,-3)

 

[tiny-tim]

Welcome to PF!

Hi dola! Welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

Try (a) first. ​

 

[dola]

Find a nonzero vector u with initial point P(-1.3.-5) such that
(a) u has the same direction as v = (6,7,-3)
(b) u is oppositely directed to v = (6,7,-3)

---->
Let, the terminal point of u is Q(x,y,z)
Thus u = vector PQ = (x+1, y-3, z+5)

(a) u will have the same direction as v
so, (x+1, y-3, z+5) = (6,7,-3)

x = 5, y = 10, z = -8

Thus one possible ans might be Q(5,10,-8)

(b) u will have the opposite direction as v
so, (x+1, y-3, z+5) = (-6,-7,3)

x = -7, y = -4, z = -2

Thus one possible ans might be Q(-7, -4, -2)


I am not sure whether the procedure is correct. Waiting for explanation

 

[tiny-tim]

… I am not sure whether the procedure is correct. Waiting for explanation

Yup, that's fine … both method and result!

 

[dola]

Thank you