​ 1. Find . Find the vector equation of line L. Find a point on line L other than C. ​

Question

From the following figure

1. Find \(\overline{AB}\).
2. Find the vector equation of line L.
3. Find a point on line L other than C.

Answer 1

1. P.v of A = i – j + 4k,

P.v. of B = 2i + j + 2k

\(\overline {AB}\) = p. v. of B – p. v. of A

= 2i + j + 2k -(i – j + 4k) = i + 2j – 2k.

2. The line L passes through (1, -2, -3) and parallel to \(\overline{AB}\)

3. From (1) of part (ii), we have

xi + yj + zk = (l + λ)i + (-2 + 2λ)j + (-3 – 2λ)k

Put λ = 1

⇒ xi +yj + zk = (1 +1)i + (-2 + 2)j + (-3 – 2 )k

⇒ xi + yj + zk = 2i + 0j – 5k

Therefore a point on line L is (2, 0, -5).