Question

2. Find the vector equations of the following lines:

a. A=(6,5,7),m=2i+5j–k
b. A=(8,6,2),B=(3,4,1)

Answer 1

a) The vector equation

`AB^(-) = -4i^(-) -0j^(-) -8k^(-)`

b) The vector equation

`AB^(-) = -5i^(-) -2j^(-) -k^(-)`

Explanation:

Step(i):-

a)

Given that the points are A( 6,5,7) and B = m = 2i+5j-k

OA = 6i+5j+7k and OB = 2i+5j-k

AB = OB-OA

= 2i+5j-k - (6i+5j+7k)

= 2i -6i +5j-5j-k-7k

=
`-4i^(-) -0j^(-) -8k^(-)`

b)

Given that the points are A( 8,6,2) and B = (3,4,1)

OA = 8i+6j+2k and OB = 3i+4j+k

AB = OB-OA

= 3i+4j+k -(8i+6j+2k)

= 3i -8i +4j-6j+k-2k

=
`-5i^(-) -2j^(-) -k^(-)`