Question

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane `vecr * (hati + 2hatj + 5hatk) + 9` = 0

पर्याय

• `hati + 2hatj + 3hatk + lambda(hati + 2hatj - 5hatk)`

• `(hati + 2hatj + 3hatk)lambda`

• `hati + 2hatj + lambda(hati + 2hatj)`

• None of these

Answer 1

`hati + 2hatj + 3hatk + lambda(hati + 2hatj - 5hatk)`

Explanation:

Direction ratios of the normal of the plane `vecr * (hati + 2hatj - 5hatk) + 9` = 0 are 1, 2, – 5.

The equation of a line passing through and with a ratio of direction b₁, b₂, b₃ is

`vecr = vecr_1 + (b_1 hati + b_2 hatj + b_3 hatk)`

Hence the line passing through (1, 2, 3) and having the direction ratios 1, 2, – 5 is

`vecr = hati + 2hatj + 3hatk + lambda(hati + 2hatj - 5hatk)`