F.5 A.maths---Vectors

Let vector AC be xu + yv, where x and y are some positive values and u and v are the given vectors.

Then dividing u and v into components of along the direction of AC and perperdicular to AC, we have:

x cos 25(deg) + y cos 40(deg) = 10 --> (1), which is along the direction of AC
x sin 25(deg) - y sin 40(deg) = 0 --> (2), which is perpendicular to the direction of AC and supposed to be zero

Rewriting (2) as y = x [sin 25(deg)/sin 40(deg)] and substituting it into (1), we have
x cos 25(deg) + x [sin 25(deg)cos 40(deg)/sin 40(deg)] = 10
x [cos 25(deg) + sin 25(deg)/tan 40(deg)] = 10
x = 7.09

Sub the result into (2), we have
y = 7.09 [sin 25(deg)/sin 40(deg)]
= 4.66

Thus, vector AC = 7.09u + 4.66v

盡一點自己的綿力, 希望能作出多一點的貢獻

let the vectors making angles of 25(degree) is xu where x is the magnitude
then
x(cos25)=10
x=11.034
let the vectors making angles of 40(degree) is yv where y is the magnitude
then
y(c0s40)=10
y=13.054
so
AC=11.034u+13.054v