Specialist math questions

[muzteka]

A and B are points defined by the position vectors a= 4i + j ad b = i-j-k respectively. Find:
a) the vector resolute of a in the direction of b
b) the component vector of a perpendcular to b
c) the shortest distance from A to OB

I need help with these questions, cant do any 

[Over9000]

Ok for a) you need to use the formula for this b
a.b = 4-1 = 3 and b.b = 1+1+1 = 3
Therefore the vector resolute is (i-j-k)

b) The perpendicular component is a- vector resolute
so 4i + j - (i-j-k) = 3i + 2j + k

c) find the magnitude which is

[muzteka]

Thanks over9000, just one extra question though.
how do you verify that a=i-3j-2k and b= 5i +j +k are two vectors perpendicular to each other

[kurrymuncher]

use the dot product between them. if they are perpendicular then the dot product should be 0

[Over9000]

Well, remember that if a.b = 0 that means that, a and b are perpendicular
so a = i - 3j - 2k and b = 5i + j + k
a.b = 5-3-2=0
Therefore they are perpendicular

[muzteka]

Thanks, I needed the working out, sometimes I just can't think