angle between a vector and a plane

[enpassant]

find the angle between 2i + (sqrt6)j - 2k and the z-x plane.

[Mao]

the x and z coordinates of this vector 2 and -2 respectively.

if we draw a right-angled triangle from this vector perpendicular to the z-x plane:

base

then

[nanie369]

blinnin

[dusty_girl1144]

is there a way someone can draw this diagram for me? im not picturing it correctly i dont think... ty

[Mao]

here you go

[dcc]

For anyone interested, there was actually a question which required this type of thinking on last years Examination 2.  A question on airplanes and stuff.

[dusty_girl1144]

here you go

you so smart... 99.95 for mao!

[aksman]

I think you could also use the vector j co-efficient (i.e sqrt6) and sin (theta) instead of having to find the base using the i and k co-efficients.
Makes life so much easier

stupid blinnin kitai

[Mao]

yes you can [and then do 90 degrees - ANS]

but that was done in april before i learnt all the tricks

[aksman]

uhhm...you don't need to do [90 degrees - ANS] because you still get the same angle but using sine instead of cosine

[Mao]

oh yes.
of course

[though i've always avoided using sine for vectors because angles in Q1 and Q2 can return the same value, though that has no impact on this question]