Question

If `vecx` and `vecy` be two non-zero vectors such that `|vecx + vecy| = |vecx|` and `2vecx + λvecy` is perpendicular to `vecy`, then the value of λ is ______.

Options

• 0

• 1

• 2

• 3

Answer 1

If `vecx` and `vecy` be two non-zero vectors such that `|vecx + vecy| = |vecx|` and `2vecx + λvecy` is perpendicular to `vecy`, then the value of λ is 1.

Explanation:

∵ `|vecx + vecy| = |vecx|`

Squaring both sides we get

`|vecx|^2 + 2vecx.vecy + |vecy|^2 = |vecx|^2`

`\implies 2vecx.vecy + vecy.vecy` = 0  ...(i)

Also `2vecx + λvecy` and `vecy` are perpendicular

∴ `2vecx.vecy + λvecy.vecy` = 0  ...(ii)

Comparing (i) and (ii), λ = 1