VEctors Questions! Help!

[1i1ii1i]

i am really struggling with a lot of vector questions and i cant understand it. please help me someone
13. A and B are points defined by the positions vectors a=i+j+k and b=2i+j-k respectively. M is the midpoint of AB.
Find: angle AOM and angle BMO

how do i work out the angle between 2 vectors??

7. A and B are points defined by the position vectors a=i+3j-k and b=j+k
Find a unit vector through A perpendicular to OB (how the eff do i do this??)


8. A and B are points defined by the position vectors a=4i+j and b=i-j-k respectively.
a) the vector compenent of a per[endicular to b
b) the shortest distance from a to OB

I AM ABSOLUTELY CLUELESS ANY ADVICE WOULD HELP ALOT! thankx

[TrueTears]

1. When you need to find the angle between 2 vectors, always think about dot product, since that contains the cosine of the angle, then sketch a diagram to know exactly which angle it is referring to (since dot product is defined by tail to tail of the vectors).

2. If you sketch a diagram, it all becomes clear, basically it is asking for the perpendicular component of a with regards to b, in other words, find the vector resolute of a in the direction of b first, then use a - (that vector) to get the perpendicular vector, then normalise this vector to find the unit vector.

3. Similar to 2. basically sketch a diagram, so first find out the vector resolute of a in the direction of b, then use a - (that vector) to get the perpendicular component. For part b, I assume you want to find the shortest distance from point A to B, then just find the vector AB and find it's magnitude, shortest distance is always a straight line.

[1i1ii1i]

thankx, could someone do working out?

[pi]

SORRY!

Oops, moved to the wrong state by accident! TT, could you move it to the "correct" spesh board in VCE please

[TrueTears]

SORRY!

Oops, moved to the wrong state by accident! TT, could you move it to the "correct" spesh board in VCE please

Done

Moderator action: removed real name, sorry for the inconvenience