Scalar and vector products 285
isparallel tothevector2i+ 7 j− 4 k. Determine
the point on the line corresponding toλ=2in
the resulting equation.
⎡
⎣r=( 5 + 2 λ)i+( 7 λ− 2 )j
+( 3 − 4 λ)k;
r= 9 i+ 12 j− 5 k⎤
⎦- Express the vector equation of the line in
problem 1 in standard Cartesian form.
[
x− 5
2
=y+ 2
7=3 −z
4=λ]In problems 3 and 4, express the given straight line
equations in vector form.3.3 x− 1
4=5 y+ 1
2=4 −z[^3
r=^13 ( 1 + 4 λ)i+^15 ( 2 λ− 1 )j
+( 4 − 3 λ)k]- 2x+ 1 =
1 − 4 y
5=3 z− 1[^4
r=^12 (λ− 1 )i+^14 ( 1 − 5 λ)j
+^13 ( 1 + 4 λ)k]