Cho tam giác ABC, M, N, P được xác định bởi véctơ MA = -3/4 BM, AN = - 3CN, CP = 1/4 PB

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Cho tam giác ABC, M, N, P được xác định bởi véctơ MA = -3/4 BM, AN = - 3CN, CP = 1/4 PB

Bài 1. Cho tam giác ABC, M, N, P được xác định bởi véctơ

MA=-34BM, .Chứng minh M, N, P thẳng hàng?

Lời giải:

Ta có: stack M A with rightwards arrow on top equals fraction numerator negative 3 over denominator 4 end fraction stack B M with rightwards arrow on top equals 3 over 4 stack M B with rightwards arrow on top comma space stack A N with rightwards arrow on top equals negative 3 stack C N with rightwards arrow on top equals 3 stack N C with rightwards arrow on top comma space stack C P with rightwards arrow on top equals 1 fourth stack P B with rightwards arrow on top

Ta lại có: stack M N with rightwards arrow on top equals stack M A with rightwards arrow on top plus stack A N with rightwards arrow on top equals 3 over 4 stack M B with rightwards arrow on top plus 3 stack N C with rightwards arrow on top equals 3 over 4 stack M P with rightwards arrow on top plus 3 over 4 stack P B with rightwards arrow on top plus 3 stack N P with rightwards arrow on top plus 3 stack P C with rightwards arrow on top

left right double arrow stack M N with rightwards arrow on top equals 3 over 4 stack M P with rightwards arrow on top plus 3 stack C P with rightwards arrow on top plus 3 stack N P with rightwards arrow on top minus 3 stack C P with rightwards arrow on top equals 3 over 4 stack M P with rightwards arrow on top plus 3 stack N P with rightwards arrow on top

left right double arrow stack M P with rightwards arrow on top plus stack P N with rightwards arrow on top equals 3 over 4 stack M P with rightwards arrow on top plus 3 stack N P with rightwards arrow on top

v equals fraction numerator increment d over denominator increment t end fraction equals 6 over 3 equals 2 space left parenthesis m divided by s right parenthesis

Do đó M, N, P thằng hàng. 

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