Question

A unit vector is represented as `(0.8hat"i" + "b"hat"j" + 0.4hat"k")`. Hence the value of 'b' must be ______.

Options

• 0.4

• `sqrt0.6`

• 0.2

• `sqrt0.2`

Answer 1

A unit vector is represented as `(0.8hat"i" + "b"hat"j" + 0.4hat"k")`. Hence the value of 'b' must be `underlinebb(sqrt0.2)`.

Explanation:

Magnitude of unit vector = 1

`sqrt((0.8)^2+("b")^2+(0.4)^2)` = 1

⇒ `sqrt(64+"b"^2+0.16)` = 1

⇒ `sqrt(0.80+"b"^2)` = 1

⇒ 0.8 + b² = 1

⇒ b² = 0.2

∴ b = `sqrt0.2`