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how to dot product two vectors with different planes?

I have vectors $A$,$B$ and $C$, vectors $A$ and $B$ is on $xy$ plane while vector $C$ is on $xz$ plane. I need to find the dot product of $A.C$ how should I do that? my book says that dot product of two vectors can be expressed in terms of their rectangular components. vector $B$ lies in $y$-axis. vector $A$ makes $60$ degrees to $B$, vector $C$ makes $37$ degrees to $x$-axis. $A=10$, $B=8$ and $C=5$.

please help me to solve this problem

Semiclassical
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nicy12
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    Dot product in Cartesian/rectangular coordinates: $(a_1,a_2,a_3)\cdot(b_1,b_2,b_3)=a_1b_1+a_2b_2+a_3b_3$. – anon May 21 '13 at 05:10

1 Answers1

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B lies in y- axis , then A makes 30 degrees with x-axis, so that:
$$A=10\cos30\, i+10\sin30\,j\qquad A=5\sqrt3\,i+5\,j$$
$$C=5\cos37\,i+5\sin37\,k\quad =4\,i+3\,k$$
$$A.C=20\sqrt3$$

RETAS
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  • please explain why A=10cos30i + 10sin30j and C=5cos37i + 5sin37k – nicy12 May 21 '13 at 05:51
  • A makes 60 degrees with B, and B lies in y-axis, then the angle between A and the x-axis is $90-60=30$, C lies in the xz plane so it has x component (i) and z-component (k). – RETAS May 21 '13 at 05:56
  • why does C has no y-component? is it because it only lies to x-z plane? – nicy12 May 21 '13 at 06:03
  • yes, nothing else. – RETAS May 21 '13 at 06:05
  • how about if the vector C lies in x-y-z plane? how do i find the components of C? – nicy12 May 21 '13 at 06:07
  • See this http://mathworld.wolfram.com/SphericalCoordinates.html – RETAS May 21 '13 at 06:11
  • thank you sir for your help and the link.. i appreciate the link you gave even it is spherical coordinate system. i only know rectangular coordinate system. thank you again – nicy12 May 21 '13 at 06:14