First slide

Dot product or scalar product of vectors

Question

$In a triangle ABC, if | \vec{B C} | = 8, | \vec{C A} | = 7, | \vec{A B} | = 10, then the projection of the vector$ $\vec{A B} on \vec{A C} is equal to:$

Moderate

A

$\frac{115}{16}$
B

$\frac{85}{14}$
C

$\frac{25}{4}$
D

$\frac{127}{20}$

Solution

$\cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{7^{2} + 10^{2} - 8^{2}}{2. (7) . (10)} = \frac{85}{140}$
$AD = Projection of \vec{A B} on \vec{A C} = 10 \cos A = 10 \times \frac{85}{140} = \frac{85}{14}$

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