![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
vector A=3i+4j is a vector in xy plane,
\n" ); document.write( "vector B is a vector perpendicular to vector A,
\n" ); document.write( "what will be the vector C equal to,which has projections 1 and 2 along vectors A and B?
\n" ); document.write( "LET C BE Pi+Qj....
\n" ); document.write( "PROJECTION OF C ALONG A =1=A.C/|A|=(3i+4j).(Pi+Qj)/|(3i+4j)
\n" ); document.write( "=(3P+4Q)/SQRT.(3^2+4^2)=(3P+4Q)/5=1
\n" ); document.write( "3P+4Q=5....................................I
\n" ); document.write( "BUT PROJECTION OF C ALONG A =1=|C|*COS(X) WHERE X IS THE ANGLE BETWEEN VECTORS A AND C.
\n" ); document.write( "HENCE COS(X)=1/|C|
\n" ); document.write( "SINCE B IS PERPENDICULAR TO A WE HAVE ANGLE BETWEEN C AND B =90-X\r
\n" ); document.write( "\n" ); document.write( "PROJECTION OF C ALONG B =2=|C|*COS(90-X)=|C|*SIN(X)
\n" ); document.write( "SQUARING WE GET ..4=|C|^2*{SIN(X)}^2 = |C|^2*{1-(COS(X))^2}=|C|^2*{1-1/|C|^2}=|C|^2-1
\n" ); document.write( "|C|^2=4+1=5
\n" ); document.write( "P^2+Q^2=5 ..II
\n" ); document.write( "SUBSTITUTING FOR Q FROM EQN.1,WE GET
\n" ); document.write( "P^2+(5-3P)^2/4^2=5
\n" ); document.write( "16P^2+25+9P^2-30P=80
\n" ); document.write( "25P^2-30P-55=0
\n" ); document.write( "5P^2-6P-11=0
\n" ); document.write( "5P^2-11P+5P-11=0
\n" ); document.write( "P(5P-11)+1(5P-11)=0
\n" ); document.write( "(P+1)(5P-11)=0
\n" ); document.write( "P=-1 ..OR .11/5
\n" ); document.write( "FROM EQN.I,WE GET
\n" ); document.write( "Q=(5-3P)/4=(5+3)/4=2 ..OR (5-3*11/5)/4=-2
\n" ); document.write( "HENCE VECTOR C IS
\n" ); document.write( "-i+2j ..OR .11i/5-2j
\n" ); document.write( "WE FIND BY CROSS CHECKING THAT 11i/5-2j IS AN EXTRANEOUS SOLUTION NOT COMPATILE WITH |C|=SQRT.5.
\n" ); document.write( "HENCE VECTOR C IS -i+2j \n" ); document.write( "