CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

In a right-angled triangle ABC, if the hypotenuse AB = p, then what is $$\overrightarrow{AB}. \overrightarrow{AC} + \overrightarrow{BC}. \overrightarrow{BA} + \overrightarrow{CA} . \overrightarrow{CB}$$ equal to?


A
p
loader
B
p2
loader
C
2p2
loader
D
p22
loader

Solution

The correct option is B $$p^2$$
$$\overrightarrow{AB}.\overrightarrow{AC}+\overrightarrow{BC}.\overrightarrow{BA}+\overrightarrow{CA}.\overrightarrow{CB}$$
$$=\overrightarrow{AB}.\overrightarrow{AC}-\overrightarrow{BC}.\overrightarrow{AB}+0$$            ...($$\overrightarrow{CA}{\bot }\overrightarrow{CB}$$)
$$=\overrightarrow{AB}.\overrightarrow{AC}+\overrightarrow{CB}.\overrightarrow{AB}$$
$$=\overrightarrow{AB}.(\overrightarrow{AC}+\overrightarrow{CB})$$
$$=\overrightarrow{AB}.(\overrightarrow{AB})$$
$$=|\overrightarrow{AB}|^2$$
$$=p^2$$

Answer is option (B)

850865_630653_ans_0351530e498641e4b22dc4e8f22c0a06.png

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image