Question

If vector equation of the line `(x - 2)/2 = (2y - 5)/-3 = z + 1  "is"  barr = (2hati + 5/2 hatj - hatk) + lambda (2hati - 3/2 hatj + phatk)` then p is equal to ______.

Options

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Answer 1

If vector equation of the line `(x - 2)/2 = (2y - 5)/-3 = z + 1  "is"  barr = (2hati + 5/2 hatj - hatk) + lambda (2hati - 3/2 hatj + phatk)` then p is equal to 0.

Explanation:

The given line is

`(x - 2)/2 = (2y - 5)/-3 = z + 1`,

= `(x - 2)/2 = (y - 5/2)/(-3/2) = (z + 1)/0`

This shows that the given line passes through the point `(2, 5/2, -1)` and has direction ratios `(2, -3/2, 0)`. Thus, given line passes through the point having position vector `bara = 2hati + 5/2 hatj - hatk` and is parallel to the vector `barb = (2hati - 3/2 hatj - 0hatk)`.

So, its vector equation is `barr = (2hati + 5/2 hatj - hatk) + lambda (2hati - 3/2 hatj - 0hatk)`.

Hence, p = 0