CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The angle between a line with direction ratio $$2 : 2 : 1$$ and a line joining $$(3, 1, 4)$$ to $$(7, 2, 12)$$ is


A
cos123
loader
B
cos132
loader
C
tan123
loader
D
None of these
loader

Solution

The correct option is A $$\cos^{-1}\dfrac23$$
Direction ratio of the line joining $$(3,1,4)$$ and $$(7,2,12)$$ be $$((7-3),(2-1),(12-4))$$ i.e. $$(4,1,8).$$
Let angle between the two be $$\theta.$$
$$(2\hat i+2\hat j+\hat k).(4\hat i+\hat j+8\hat k)=|2\hat i+2\hat j+\hat k||4\hat i+\hat j+8\hat k|\cos\theta$$
$$\Rightarrow 8+2+8=3\times9\cos\theta$$
$$\Rightarrow \cos \theta=\dfrac{18}{27}=\dfrac23$$
$$\Rightarrow \theta=\cos^{-1}\dfrac23$$
Hence, A is the correct option.

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image