Vector Algebra
Scalar product
Grade 12

Question:

<p>OP · OQ, where O is the origin (P is on the circle and curve, Q is inside the circle with integer abscissa)</p>
<p>(a) 4 or 7</p>
<p>(b) 4 or 2</p>
<p>(c) 2 or 3</p>
<p>(d) 7 or 8</p>

Step-by-Step Solution

Key Concept: The dot product depends on the coordinates of both P and Q, where Q's position is constrained by being inside the circle with integer abscissa.
Using the dot product formula for position vectors from origin, and considering the constraints on P and Q (P on circle, Q inside circle with integer x-coordinate), the dot product OP · OQ can be either 4 or 2.
Correct Answer: b

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