In a triangle ABC with usual notations,if |ov | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the sides of the triangle be $a = |\overline{BC}| = 8$,$b = |\overline{CA}| = 7$,and $c = |\overline{AB}| = 10$. We need to find the projectio

Vedclass · Accepted Answer

$\frac{85}{14}$ units

Vedclass · Answer

(C) Let the sides of the triangle be $a = |\overline{BC}| = 8$,$b = |\overline{CA}| = 7$,and $c = |\overline{AB}| = 10$. We need to find the projection of $\overline{AB}$ on $\overline{AC}$. In $	riangle ABC$,by the Law of Cosines,we have $a^2 = b^2 + c^2 - 2bc \cos(A)$. Substituting the values,$8^2 = 7^2 + 10^2 - 2(7)(10) \cos(A)$. $64 = 49 + 100 - 140 \cos(A)$. $64 = 149 - 140 \cos(A)$. $140 \cos(A) = 149 - 64 = 85$. $\cos(A) = \frac{85}{140} = \frac{17}{28}$. The projection of vector $\overline{AB}$ on $\overline{AC}$ is given by $|\overline{AB}| \cos(A)$. Projection $= 10 	imes \frac{17}{28} = \frac{170}{28} = \frac{85}{14}$ units.

In a triangle $ABC$ with usual notations,if $|\overline{BC}|=8, |\overline{CA}|=7, |\overline{AB}|=10$,then the projection of $\overline{AB}$ on $\overline{AC}$ is

Similar Questions

The projection of the vector $2i + j - 3k$ on the vector $i - 2j + k$ is:

The altitude through vertex $A$ of $\triangle ABC$ with position vectors of points $A, B, C$ as $\bar{a}, \bar{b}, \bar{c}$ respectively is

If the vectors $ai + bj + ck$ and $\pi + qj + rk$ are perpendicular, then

If $a, b, c$ are non-coplanar vectors,then the point of intersection of the line passing through the points $2a+3b-c$ and $3a+4b-2c$ with the line joining the points $a-2b+3c$ and $a-6b+6c$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module