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Suppose you are given two points, \(A(17,19)\) and \(B(11,13)\). Find the position vector \( \vec{AB} \).

Which of the following operations are not allowed on vectors?

I. Addition

II. Subtraction

III. Multiplication

IV. Division

Suppose a vector \(v=2i-14j\). Find the unit vector \(u\) which has the same direction as \(v\).

Find the sum of numbers less than 10,000 formed with the digits 0, 2, 4, 6 and 8.

Note: No digits are allowed to be repeated.

If \(q \neq 1\) and \(n\) is a positive integer,

\(\large a + aq + {aq}^2 + {aq}^3 + \dots + {aq}^n = a \frac {1-q^{n+1}}{1-q}\)

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