Question

If `|bar"a"| = |bar"b"| = 1, bar"a"*bar"b" = 0` and `bar"a" + bar"b" + bar"c" = bar"0"`, then `|bar"c"|` is equal to ______.

Options

• 1

• `sqrt(2)`

• `sqrt(3)`

• `sqrt(5)`

Answer 1

If `|bar"a"| = |bar"b"| = 1, bar"a"*bar"b" = 0` and `bar"a" + bar"b" + bar"c" = bar"0"`, then `|bar"c"|` is equal to `sqrt(2)`.

Explanation:

`bar"a" + bar"b" + bar"c" = bar"0"`

⇒ `bar"a" + bar"b" = - bar"c"`

Squaring on both sides, we get

`|bar"a" + bar"b"|^2 = |bar"c"|^2`

⇒ `|bar"a"|^2 + 2bar"a"*bar"b" + |bar"b"|^2 = |bar"c"|^2`

⇒ `1^2 + 2(0) + 1^2 = |bar"c"|^2`

⇒ `|bar"c"|^2` = 2

⇒ `|bar"c"| = sqrt(2)`