JEE Mains · Maths · STD 12 - 10. vector algebra
In a triangle \(ABC ,\) if \(|\overline{ BC }|=8,|\overline{ CA }|=7,|\overline{ AB }|=10,\) then the projection of the vector \(\overline{ AB }\) on \(\overline{ AC }\) is equal to ....... .
- A \(\frac{25}{4}\)
- B \(\frac{85}{14}\)
- C \(\frac{127}{20}\)
- D \(\frac{115}{16}\)
Answer & Solution
Correct Answer
(B) \(\frac{85}{14}\)
Step-by-step Solution
Detailed explanation
\(|\vec{a}|=8,|\vec{b}|=7,|\vec{c}|=10\) \(\cos \theta=\frac{|\vec{b}|^{2}+|\vec{c}|^{2}-|\vec{a}|^{2}}{2|\vec{b}||\vec{c}|}=\frac{17}{28}\) Projection of \(\overrightarrow{ c }\) on \(\overrightarrow{ b }\) \(=|\overrightarrow{ c }| \cos \theta\) \(=10 \times \frac{17}{28}\)…
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