Question

Se dau vectorii

v1= 3i - 4j
v2= (1-m)i + (2m-3)j

a) determinati m astfel incat v1 perpendicular pe v2

b) pentru m= -1, calculati cos de alfa​

Answer 1

Răspuns:

2 vectori sunt perpendiculari daca produsul lor scalar e  0.

pui conditia ca  v1*v2-0

v1*v2=(3i-4j)[(1-m)i+(2m-3)j]=0

3(1-m)i²-4(2m-3)j²=      i²=j²=1   ij=ji=0

3(1-m)i²-8m+12=

3-3m-8m+12=

-11m+15=0

-11m=-15

m=-15/(-11)=15/11

b)m= -1

v2=(1-(-1))i+(2*(-1)-3)j=

(1+1)i+(-2-3)j=

2i-5j

v1*v2=(3i-4j)(2i-5j)=6i²-4*(-5)j²=6+20=26 (A

dar v1*v2=lv1l*lv2l*cos<(v1*v2)

lv1l=√[3²+(-4)²]=√(9+16)=√25=5

lv2l=√(2²+5²)=√29

26=5*√29*cos(<v1*v2)

cos(v1;v2)=26/5√29

Explicație pas cu pas: