4.7.6 Vektor, SPM Praktis (Kertas 2) Posted on May 14, 2020 by Myhometuition Soalan 6:Diagram below shows a trapezium OABC and point D lies on AC. Diberi bahawa OC → =18 b ˜ , OA → =6 a ˜ dan OC → =2 AB → . (a) Ungkapkan dalam sebutan a ˜ dan b ˜ , (i) AC → (ii) OB → (b) Diberi bahawa AD → =k AC → , dengan keadaan k ialah pemalar. Cari nilai k jika titik-titik O, D dan B adalah segaris. Penyelesaian: (a)(i) AC → = AO → + OC → =−6 a ˜ +18 b ˜ =18 b ˜ −6 a ˜ (a)(ii) OC → =2 AB → 18 b ˜ =2( AO → + OB → ) 18 b ˜ =2( −6 a ˜ + OB → ) 18 b ˜ =−12 a ˜ +2 OB → OB → =6 a ˜ +9 b ˜ (b) OD → =h OB → =h( 6 a ˜ +9 b ˜ ) =6h a ˜ +9h b ˜ AD → = OD → − OA → =6h a ˜ +9h b ˜ −6 a ˜ = a ˜ ( 6h−6 )+9h b ˜ AD → =k AC → a ˜ ( 6h−6 )+9h b ˜ =k( 18 b ˜ −6 a ˜ ) a ˜ ( 6h−6 )+9h b ˜ =−6k a ˜ +18k b ˜ 6h−6=−6k h−1=−k h=1−k..........( 1 ) 9h=18k h=2k Dari ( 1 ), 1−k=2k 3k=1 k= 1 3
