Question

The vector equation of the line passing through the point having position vector `4 hat i - hat j + 2hat k` and parallel to vector `-2 hat i - hat j + hat k` is given by ______.

Options

• `(4hat i - hat j - 2hat k) + lambda (-2hat i - hat j + hat k)`

• `(4hat i - hat j + 2hat k) + lambda (2hat i - hat j + hat k)`

• `(4hat i - hat j + 2hat k) + lambda (-2hat i - hat j - hat k)`

• `(4hat i - hat j + 2hat k) + lambda (-2hat i - hat j + hat k)`

Answer 1

The vector equation of the line passing through the point having position vector `4 hat i - hat j + 2hat k` and parallel to vector `-2 hat i - hat j + hat k` is given by `bbunderline((4hat i - hat j + 2hat k) + lambda (-2hat i - hat j + hat k))`.

Explanation:

We know that, r = r₀ + λd

Given, `r_0 = 4 hat i - hat j + 2hat k` 

`d = -2 hat i - hat j + hat k`

Substituting these values:

`r = (4 hat i - hat j + 2 hat k) + lambda(- 2hat i - hat j + hat k)`