Question

The distance of the point with position vector `3hati + 4hatj + 5hatk` from the y-axis is ______.

Options

• 4 units

• `sqrt(34)` units

• 5 units

• `5sqrt(2)` units

Answer 1

The distance of the point with position vector `3hati + 4hatj + 5hatk` from the y-axis is `underlinebb(sqrt(34)  units)`.

Explanation:

To find the distance of a point P with coordinates (x, y, z) from oneof the coordinate axes, we use the following formulas for theperpendicular distance:

Distance from the x-axis = `sqrt(y^2 + z^2)`

Distance from the y-axis = `sqrt(x^2 + z^2)`

Distance from the z-axis = `sqrt(x^2 + y^2)`

For this question, we need the formula for distance from the y-axis.

Given, position vector = `3hati + 4hatj + 5hatk`

So, the point is P(3, 4, 5).

Applying the formula:

Distance from the y-axis = `sqrt(x^2 + z^2)`

Putting x = 3 and z = 5

= `sqrt(3^2 + 5^2)`

= `sqrt(9 + 25)`

= `sqrt(34)` units