If the position vector a of a point (12, n) is such that |vector a|= 13, find the value(s) of n.

Question

If the position vector \(\vec a\) of a point (12, n) is such that |\(\vec a\)|= 13, find the value(s) of n.

Answer 1

Given \(\vec a\) is the position vector of point (12, n).

We know position vector of a point (x, y) is given by \(\text x\hat i+y\hat j\), where \(\hat i\) and \(\hat j\) are unit vectors in X and Y directions.

⇒ \(\vec a\)= 12\(\hat i+n\hat j\)

Now, we need to find n such that \(|\vec a|=13\).

Recall the magnitude of the vector \(\text x\hat i+y\hat j\) is given as

Squaring both the sides, we have

Thus, n = 5 or -5

Answer 2

we consider positive values hence neglecting -5