Question

For any vector `overlinex` the value of `(overlinex xx hati)^2 + (overlinex xx hatj)^2 + (overlinex xx hatk)^2` is equal to ______

Options

• `|overlinex|^2`

• `2|overlinex|^2`

• `3|overlinex|^2`

• `4|overlinex|^2`

Answer 1

For any vector `overlinex` the value of `(overlinex xx hati)^2 + (overlinex xx hatj)^2 + (overlinex xx hatk)^2` is equal to `underline(2|overlinex|^2)`

Explanation:

`|x xx i|^2 = |(hati, hatj, hatk), (x_1, x_2, x_3), (1, 0, 0)|` ................[∵ x = `x_1hati + x_2hatj + x_3hatk`]

= `|x_3hatj - x_2hatk|^2 = x_3^2 + x_2^2`

Similarly, `|overlinex xx hatj|^2 = x  x xx_1^2 + x_3^2` and `|overlinex + hatk|^2 = x_1^2 + x_2^2`

Hence, the required result is

= `2(x_1^2 + x_2^2 + x_3^2) = 2|overlinex|^2`