document.write( "Question 1084399: The vector x and y are unit vectors (vectors with the magnitude 1) that make an angle of 30 degrees with each other.
\n" ); document.write( "a)calculate the value of |2x-y|
\n" ); document.write( "b)determine the direction of 2x-y \n" ); document.write( "
Algebra.Com's Answer #699905 by mathmate(429)\"\" \"About 
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Question:
\n" ); document.write( "The vector x and y are unit vectors (vectors with the magnitude 1) that make an angle of 30 degrees with each other.
\n" ); document.write( "a)calculate the value of |2x-y|
\n" ); document.write( "b)determine the direction of 2x-y
\n" ); document.write( "
\n" ); document.write( "Solution:
\n" ); document.write( "Without loss of generality, we will assume unit vector x is along the positive x-axis, and unit vector y is at +30°.
\n" ); document.write( "Therefore
\n" ); document.write( "2x-y=
\n" ); document.write( "2< 1,0 > - < cos(30),sin(30) >
\n" ); document.write( "=<2-(√2)/2, 0-1/2>
\n" ); document.write( "and
\n" ); document.write( "|2x-y|=√((2-(√2)/2)² + (-1/2)^2)
\n" ); document.write( "=1.3862\r
\n" ); document.write( "\n" ); document.write( "Angle
\n" ); document.write( "=atan((-1/2)÷(2-(√2)/2))
\n" ); document.write( "=atan(1.29289/-0.5)
\n" ); document.write( "=-0.369 radians
\n" ); document.write( "= -21.143°\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );