已知向量m的模=4,n的模为3，m与n夹角为60°，a=4m-n，b=m+2n，c=2m-3n。求解以下几题：

设m=3i+5j+8k，n=2i-4j-7k和p=5i+j-4k，求向量a=4m+3n-p在x轴上~

a=4m+3n-p
=4(3i+5j+8k)+3(2i-4j-7k)-(5i+j-4k)
=13i+7j+15k,
所以a在x轴上的投影是13，在y轴上的分向量是7j.

联立得：4m?n＝6①8m+3n＝2②，①×3+②得：20m=20，即m=1，将m=1代入①得：4-n=6，即n=-2，将m=1，n=-2代入2am-n=5得：2a+2=5，解得：a=32．故选B

（1）向量a^2=(4m-n)^2=16m^2-8mn+n^2=256-96+9=169
向量b^2=m^2+4mn+4n^2=16+48+36=100
向量c^2=4m^2-12mn+9n^2=64-144+81=1
所以向量a^2+向量b^2+向量c^2=270
（2）ab=4m^2+7mn-2n^2=64+84-18=130
2bc=4m^2+2mn-12n^2=64+24-108=-20
3ca=24m^2-42mn+9n^2=-39
所以ab+2bc-3ca=71
兄弟打得真是累啊，给点分吧

按这 M向量*N向量=m的模*n的模*cosm与n夹角 计算即可

On November 8th, the voters of who live in the Los Angeles schools district will be faced with their fourth proposition,Christian Louboutin Wedges, called Measure Y. The $3.985 bond measure, which will be paid by property taxes, is for more planned expansion within the Los Angeles schools, allowing them to add another 25 elementary schools to the current list of 160 schools that are scheduled to be constructed by year 2012. Some of the money also is slated for other needs, such as new school buses, repairs and charter schools.The other three bond measures were passed for Los Angeles schools new construction and repairs that were long overdue. Classrooms were literally falling apart, and classes were excessively overcrowded with year-round schedules for many schools. The previously passed measures underwrote the current 160 schools on the list for construction.Many people, however, are asking if this fourth measure is truly needed. According to the Los Angeles Daily News, the traditional Los Angeles schools are slowly but steadily losing students from their rolls. Since the 2002-2003 school year, the traditional Los Angeles schools have lost 4,louboutin womens shoes,471 students. According to Los Angeles schools officials, they expect another 4,304 to be dropped this year. There are several reasons for these drops in enrollment.First, one in every 20 students is choosing to attend a charter or private school,Discount Christian Louboutin Shoes, rather than attend traditional Los Angeles schools. The 88 charter schools within the state now enroll about three percent (about 200,Christian Louboutin Pumps,000) of the public school students. About 35,000 of these students attend charter schools within the Los Angeles schools. The number of charter schools within the state continues to increase, with another 20 new charter schools planned for this fall.The California Charter Schools Association predicts that ten percent of public school students within the state will attend charter schools by the year 2014,Christian Louboutin Bridal Shoes, with perhaps an even higher percentage in the Los Angeles schools area. They cite that the number of charter schools would need to triple in order to accommodate all of the students currently on waiting lists. With the smaller size and flexibility of charter schools, they can be created and implemented in a very short time, as compared to the large, traditional Los Angeles schools that take years to construct.The second reason for the drastic drop in enrollment at the Los Angeles schools is birth and lifestyle trends:* Los Angeles County statistics have shown that hundreds of fewer babies are being born in the county each year. The trend is expected to continue through to the end of the decade.* Upper income singles and couples with few children have replaced neighborhoods that were once inhabited by large immigrant families. With the rising housing prices in the Los Angeles schools area, most young families or families with many children can no longer afford to live there, opting to move to areas with lower costs of living.* Additionally, according to researchers at the Public Policy Institute of California, another trend is smaller immigrant families. In their 2002 report, they show that after the first generation, immigrant families successively have smaller families.Glenn Gritzner, special assistant to the Los Angeles schools, says that the Los Angeles schools have taken the changes in demographics into consideration, but they are not critical enough to change the school building plans. Gritzner states that, if school plans and trends/statistics remain on course through 2012, there still will be 200,000 Los Angeles schools students in portable classrooms and plenty of overcrowded Los Angeles schools remaining. Plus, trends are only current patterns that are subject to change. Measure Y definitely is warranted.

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长岛县19230687918： 已知向量m的模=4,n的模为3,m与n夹角为60°,a=4m - n,b=m+2n,c=2m - 3n.求解以下几题: - ？
逄萱复洛： (1)向量a^2=(4m-n)^2=16m^2-8mn+n^2=256-96+9=169 向量b^2=m^2+4mn+4n^2=16+48+36=100 向量c^2=4m^2-12mn+9n^2=64-144+81=1 所以向量a^2+向量b^2+向量c^2=270 (2)ab=4m^2+7mn-2n^2=64+84-18=1302bc=4m^2+2mn-12n^2=64+24-108=-203ca=24m^2-42mn+9n^2=-39 所以ab+2bc-3ca=71 兄弟打得真是累啊,给点分吧

长岛县19230687918： 已知,向量m,n满足向量m的模等于3,向量n的模为4,且(m家kn)⊥(m减kn),那么实数k等 - ？
逄萱复洛： |m|=3,|n|=4 因为 (m+kn)⊥(m-kn) 所以 (m+kn)(m-kn)=0 即 m²-k²n²=0 所以 |m|²-k²|n|²=0 解得 k²=9/16,k=±3/4.

长岛县19230687918： 已知向量m,n的夹角为60°,m的模=1 n的模=2 ,向量a=3m+2n(向量), 向量b=2m - n(向量) - ？
逄萱复洛： 向量m,n的夹角为60°,m的模=1 n的模=2,mn=|m||n|cos60º=2*1*(1/2)=11.(a+b)(a-b)=(5m+n)(m+3n)=5m²+16mn+3n²=5*1²+16+3*2²=332.a+kb=x(5a-3b),5x=1,-3x=k,k=-3/53.(a+kb)⊥(5a-3b),(a+kb)(5a-3b)=0,[(3+2k)m+(2-k)n](9m+13n)=09(3+2k)m²+[9(2-k)+13(3+2k)]mn+13(2-k)n²=09(3+2k)*1²+[9(2-k)+13(3+2k)]*1+13(2-k)*2²=0 k=188/17

长岛县19230687918： 数学问题已知向量的模=4,向量的模=3,1若向量a=向量b,求向 ？
逄萱复洛： 解:已知:向量a的模=4,向量b的模=3 由向量a乘向量b=|a|*|b|*cosθ 可得: 当向量a 平行于向量b时,θ=0,则向量a乘向量b=|a|*|b|*1=12;当θ=120°时,向量a乘向量b=|a|*|b|*cos120°=-6;〔向量a-向量b〕的平方=|a|^2+|b|^2-|a|*|b|*cos120°=31; 向量a加向量b的模的值为√(|a|^2+|b|^2+|a|*|b|*cos120°)=√19

长岛县19230687918： 已知向量a=(4,3).b=( - 1,2)m=a - λb, n=2a+b 求λ等于多少时 m的模等于n的模 - ？
逄萱复洛： m=a-λb=(4+λ,3-2λ) n=2a+b=(7,8) |m|=|n|(4+λ)²+(3-2λ)²=1135λ²-4λ-88=0 λ=(2±2√111)/5

长岛县19230687918： 向量a的模为4,向量b的模为3,向量(2a - 3b)*(2a+b)=61 - ？
逄萱复洛： 1 4a^2-4ab-3b^2=614*16-4ab-3*9=61 ab=-6=|a|*|b|*cosα=12cosα cosα=-1/2 α=120度2 根据三角形余弦定里 |a+b|^2=4^2+3^2-2*4*3*cos60度=13 |a+b|=根13 |a-b|^2=4^2+3^2-2*3*4*cos120度=37 |a-b|=根373 题目字母混用

长岛县19230687918： a向量的模为4,b向量的模为3 - ？
逄萱复洛： ||||用向量叉积算面积=|a+2b|*|a-3b|sin(两向量夹角)=|(a+2b)X(a-3b)|=|aXa+2bXa-3aXb-6bXb|=|2bXa-3aXb|=|2bXa+3bXa|=5|bXa|=5|b|*|a|*sin30°=30

长岛县19230687918： 已知向量n=(a,b),向量n垂直m,且n的模=m的模,则向量m的坐标是? - ？
逄萱复洛：[答案] 设向量m=(x0,y0),向量n⊥m,则n·m=0, x0*a+y0*b=0, √(a^2+b^2)=√(x0^2+y0^2), x0=-b0y/a0, x0=b,y0=-a, 或x0=-b,y0=a, 所以向量m=(b,-a),或m=(-b,a).

长岛县19230687918： 数学向量问题~ - ？
逄萱复洛： (a+b)2=(6m-3n)2=9[4m2-4mn+n2]=9[4*8-4√8*3(√2/2)+32]=9*17|a+b|=3√17(a-b)2=(4m+7n)2=16m2+56mn+49n2=16*8+56√8*3(√2/2)+49*9=905|a-b|=...

长岛县19230687918： 已知向量m,n的夹角为60°,m的模=1 n的模=2 ,向量a=3m+2n(向量), 向量b=2m - n(向量),求向量a乘以向量b - ？
逄萱复洛： 向量a乘以向量b=(3m+2n)(2m-n)=6m^2-2n^2+mn=6-2*4+1*2*cos60°=-1 a+b=(5m+n),|a+b|=根号(25m^2+n^2+10mn)=根号(25+4+10*1*2*cos60°)=根号39 a-b=m+3n,|a-b|=根号(m^2+9n^2+6mn)=根号(1+9*4+6*1*2*cos60°)=根号43 |a+b| |a-b|=根号39*根号43=根号1677