vector interception

[james cook]

here is a question i'm not quiet sure how to do

find where these intercept

r=14i-j+#(5i-aj) and r= 9i-4j+$(-4i+6j)

# and $ are scalar multiples of the braccets

thankyou

 

[soroban]

Hello, James!

Is that really an "a" in there?
. . It makes the problem <u>very</u> messy.

BTW, the word is <u>intersect</u>.

 

[james cook]

sorry

r=14i-j+#(5i-4j)

i can't read my own writting

 

[soroban]

Hello, James!

Find where these intersect: .r = 14i - j + a(5i - 4j) .and . r= 9i- 4j + b(-4i + 6j)

a and b are scalars.

We have: .r .= .(14i - j) + a(5i - 4j) .= .(14 + 5a)i + (-1 - 4a)j
. . . . and: .r .= .(9i - 4j) + b(-4i + 6j) .= .(9 - 4b)i + (-4 + 6b)j

They intersect when the two vectors are equal . . .
. . that is, when their corresponding components are equal.

We have: .14 + 5a .= .9 - 4b . . ---> .5a + 4b .= -5 . [1]
. . . . and: . -1 - 4a .= .-4 + 6b . ---> . 4a + 6b .= .3 . [2]

We have a system of equations.

Solving [1] and [2], we get: .a = -3, b = 5/2