Two vectors ( p ) and ( q ) have magnitudes (| p |=6 ) and (| q |=8 )

MATHEMATICS · Multi-part · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Two vectors

\mathbf{p}

and

\mathbf{q}

have magnitudes

|\mathbf{p}|=6

and

|\mathbf{q}|=8

. The angle between them is

60^{\circ}

. (i) Calculate

\mathbf{p}\cdot\mathbf{q}

. (ii) If the magnitude of

\mathbf{q}

is changed to

10

while the angle remains the same, determine the new value of

\mathbf{p}\cdot\mathbf{q}

. (iii) Comment, with suitable reasoning, on how changing the magnitude of one vector affects the value of the dot product when the angle is kept fixed.

Related theory

Dot Product
Vectors
Scalar product
Vector Algebra
Dot product of two vectors

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