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標題:
發問:
A,B and C are points in a plane such that →OA=i+j,→OB=2i-5j and →AC-→CB=4i+j (a)Express →AB and →OC in tems of i and j (b)Find the angle between →AB and →OC
最佳解答:
→AB =→OB-→OA =2i-5j-i-j =i-6j// →AC-→CB=4i+j →OC-→OA-→OB+→OC=4i+j 2→OC-(i+j)-(2i-5j)=4i+j 2→OC=7i-3j →OC=(7/2)i-(3/2)j// (b)Find the angle between →AB and →OC cos (the angle between →AB and →OC )=(→AB)(→OC)/(AB)(OC) =>cos()=(i-6j)[(7/2)i-(3/2)j]/(37)^0.5 (29/2)^0.5 =>cos()=(7/2+9)/(37)^0.5 (29/2)^0.5 =>cos()=0.539666114 => the angle between →AB and →OC =57.33908725//
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AMATHS發問:
A,B and C are points in a plane such that →OA=i+j,→OB=2i-5j and →AC-→CB=4i+j (a)Express →AB and →OC in tems of i and j (b)Find the angle between →AB and →OC
最佳解答:
→AB =→OB-→OA =2i-5j-i-j =i-6j// →AC-→CB=4i+j →OC-→OA-→OB+→OC=4i+j 2→OC-(i+j)-(2i-5j)=4i+j 2→OC=7i-3j →OC=(7/2)i-(3/2)j// (b)Find the angle between →AB and →OC cos (the angle between →AB and →OC )=(→AB)(→OC)/(AB)(OC) =>cos()=(i-6j)[(7/2)i-(3/2)j]/(37)^0.5 (29/2)^0.5 =>cos()=(7/2+9)/(37)^0.5 (29/2)^0.5 =>cos()=0.539666114 => the angle between →AB and →OC =57.33908725//
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