SOLUTION: Consider the following. ๐˜‚ = ๐—ถ + 6๐—ท, ๐˜ƒ = 7๐—ถ โˆ’ ๐—ท (a) Find ๐˜‚ ยท ๐˜ƒ. ๐˜‚ ยท ๐˜ƒ = (b) Find the angle between ๐˜‚ and ๐˜ƒ to the nearest degree.

Algebra ->  Trigonometry-basics -> SOLUTION: Consider the following. ๐˜‚ = ๐—ถ + 6๐—ท, ๐˜ƒ = 7๐—ถ โˆ’ ๐—ท (a) Find ๐˜‚ ยท ๐˜ƒ. ๐˜‚ ยท ๐˜ƒ = (b) Find the angle between ๐˜‚ and ๐˜ƒ to the nearest degree.       Log On


   

Question 1206882: Consider the following.
๐˜‚ = ๐—ถ + 6๐—ท, ๐˜ƒ = 7๐—ถ โˆ’ ๐—ท
(a) Find ๐˜‚ ยท ๐˜ƒ.
๐˜‚ ยท ๐˜ƒ =

(b) Find the angle between ๐˜‚ and ๐˜ƒ to the nearest degree.
๐œƒ = ยฐ
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

u+=+i+%2B+6j, v+=+7i+-+j
(a) Find u+%2A+v

To find the dot product of u and v, use the formula
u+%2A+v=+%28a%5B1%5D+%2Aa%5B2%5D%29+%2B+%28b%5B1%5D+%2Ab%5B2%5D%29+
where a%5B1%5D, a%5B2%5D are the coefficients of i and b%5B1%5D,b%5B2%5D are the coefficients of j.

In this case,
a%5B1%5D=1, b%5B1%5D=6
a%5B2%5D=7, b%5B2%5D=-1

the dot product of u+and v is
u+%2Av+=+%281+%2A7%29+%2B+%286+%2A-1%29+=7-6=1


(b) Find the angle between u+and v to the nearest degree.
To find the angle between u+and v , we use the formula:

cos%28theta%29+=+%28u+%2Av%29%2F%28abs%28u%29%2Aabs%28v%29%29

where abs%28u%29 and abs%28v%29+are the magnitudes of u+and v , respectively
the magnitude of u is sqrt%281%5E2%2B6%5E2%29=sqrt%2837%29
the magnitude of v+is sqrt%287%5E2%2B%28-1%29%5E2%29=sqrt%2850%29

cos%28theta%29+=+1%2F%28sqrt%2837%29%2Asqrt%2850%29%29
cos%28theta%29+=+0.02324952774876386
theta+=+cos%5E-1%280.02324952774876386%29
theta+=+88.667780146130361ยฐ
theta+=+89ยฐ