Question

In a triangle ABC, if |BC| = 8, |CA| = 7, |AB| = 10, then the projection of the vector AB on AC is equal to :

• A. 115/16
• B. 85/14
• C. 127/20
• D. 25/4

Hint:

The projection of $\vec{a}$ on $\vec{b}$ is $\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|} = |\vec{a}| \cos \theta$.

Answer 1

The Correct Option is B

Step 1: Projection of $\vec{AB}$ on $\vec{AC}$ is $|\vec{AB}| \cos A$.
Step 2: Using Cosine Rule: $\cos A = \frac{b^2 + c^2 - a^2}{2bc} = \frac{7^2 + 10^2 - 8^2}{2(7)(10)}$. $\cos A = \frac{49 + 100 - 64}{140} = \frac{85}{140}$.
Step 3: Projection $= 10 \times \frac{85}{140} = \frac{85}{14}$.