document.write( "Question 852131: Given that: u = 6i−2j−8k and v = −7j−2k\r
\n" ); document.write( "\n" ); document.write( "q1) Find a vector in the same direction as u but equal in magnitude to v?
\n" ); document.write( "q2) Find a vector in the same direction as v but with a magnitude of 4? \n" ); document.write( "

Algebra.Com's Answer #513177 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
1) Find the magnitude of v first.
\n" ); document.write( " $\"abs%28v%29=sqrt%28%28-7%29%5E2%2B%28-2%29%5E2%29=sqrt%2853%29\"$
\n" ); document.write( "Find the \"u\" unit vector by dividing it by its magnitude.
\n" ); document.write( " $\"abs%28u%29=sqrt%286%5E2%2B%28-2%29%5E2%2B%28-8%29%5E2%29=sqrt%28104%29=+2%2Asqrt%2826%29\"$
\n" ); document.write( "So the u unit vector would be
\n" ); document.write( "( $\"6+%2F%282%2Asqrt%2826%29%29\"$ , $\"-2%2F%282%2Asqrt%2826%29%29\"$ , $\"-8%2F%282%2Asqrt%2826%29%29\"$ )
\n" ); document.write( "So then multiply the u unit vector by the magnitude of v.
\n" ); document.write( "( $\"%286%2Asqrt%2853%29%29+%2F%282%2Asqrt%2826%29%29\"$ , $\"%28-2%2Asqrt%2853%29%29%2F%282%2Asqrt%2826%29%29\"$ , $\"%28-8%2Asqrt%2853%29%29%2F%282%2Asqrt%2826%29%29\"$ )
\n" ); document.write( "( $\"3%2Asqrt%2853%2F26%29\"$ , $\"-sqrt%2853%2F26%29\"$ , $\"-4%2Asqrt%2853%2F26%29%29\"$ )
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\n" ); document.write( "2) The v unit vector is
\n" ); document.write( "( $\"0.0\"$ , $\"-7%2Fsqrt%2853%29\"$ , $\"-2%2Fsqrt%2853%29\"$ )
\n" ); document.write( "Just multiply this by $\"4\"$ ,
\n" ); document.write( "( $\"0.0\"$ , $\"-28%2Fsqrt%2853%29\"$ , $\"-8%2Fsqrt%2853%29\"$ )
\n" ); document.write( "( $\"0.0\"$ , $\"-%2828%2F53%29%2Asqrt%2853%29\"$ , $\"-%282%2F53%29%2Asqrt%2853%29\"$ ) \n" ); document.write( "

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