Question

If position vector `vecP` of a point (24, n) is such that `vec|P|` = 25, then the value of n is ______.

विकल्प

• ±49

• ±5

• ±1

• ±7

Answer 1

If position vector `vecP` of a point (24, n) is such that `vec|P|` = 25, then the value of n is ±7.

Explanation:

A position vector `vec("P")` for a point (x, y) is given by:

`vec P = xhat"i" + yhat"j"`

For the point (24, n) the vector is:

`vec P = 24hat"i" + nhat"j"`

The magnitude (length) of a vector `vec P` calculated as:

`|vec P| = sqrt(x^2 + y^2)`

Substituting the values:

25 = `sqrt(24^2 + n^2)`

Solve for n

25² = 24² + n²    ...(Square both sides)

625 = 576 + n²

n² = 625 − 576 ...(Subtract 576 from both side)

n² = 49

n = ±`sqrt49`

n = ±7