Define direction cosines of a direction line. - Vidyadip

Question

Define direction cosines of a direction line.

✓

Answer

The direction cosines of a direction line segment are the cosines of the direction angles of the line segment. Let two points $A(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ define the directed line segment AB.
The direction cosines of AB are given by cos
$\alpha=\frac{\text{x}_2-\text{x}_1}{\text{d}}$
$\cos\beta=\frac{\text{y}_2-\text{y}_1}{\text{d}}$
$\cos\gamma=\frac{\text{z}_2-\text{z}_1}{\text{d}}$
Here, d is the distance between A and B.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Direction Cosines and Direction Ratios→Direction Cosines and Direction Ratios — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $A =\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$ and $A (\operatorname{adj} A )= KI$, then the value of ' $K$ ' is .....

Evaluate:
$\text{cosec}\Big\{\cot^{-1}\Big(-\frac{12}{5}\Big)\Big\}$

Evaluate:
$\int\Big(\frac{2\cos^2\text{x}-\cos2\text{x}}{\cos^2\text{x}}\Big)\text{dx}$

Write a vector satisfying $\vec{\text{a}}.\hat{\text{i}}=\vec{\text{a}}.\big(\hat{\text{i}}+\hat{\text{j}}\big)=\vec{\text{a}}.\big(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}\big)=1.$

If $f: R \rightarrow R$ is given by $f(x)=x^3$, write $f^{-1}(1)$.

If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are non-coplanar vectors, then find the value of $\frac{\vec{\text{a}}.\big(\vec{\text{b}}\times\vec{\text{c}}\big)}{\big(\vec{\text{c}}\times\vec{\text{a}}\big).\vec{\text{b}}}+\frac{\vec{\text{b}}.\big(\vec{\text{a}}\times\vec{\text{c}}\big)}{\vec{\text{c}}.\big(\vec{\text{a}}\times\vec{\text{b}}\big)}$

In $\triangle ABC$, prove that $( b - c )^2 \cos ^2\left(\frac{ A }{2}\right)+( b + c )^2 \sin ^2\left(\frac{ A }{2}\right)= a ^2$

If $\vec{\text{a}}$ is a vector and m is a scalar such that m $\vec{\text{a}}=\vec0$, then what are the alternatives for m and $\vec{\text{a}}$?

Prove that the volume of a parallelepiped whose coterminous edges as $\bar{a}, \bar{b}, \bar{c}$ is $[\bar{a} \bar{b} \bar{c}]$. Hence find the volume of a parallelepiped whose coterminous edges $\bar{i}+\bar{j} \cdot \bar{j}+\bar{k}$ and $\bar{k}+\bar{i}$

Prove that the following function are increasing on R.
$f(x) = 3x^5 + 40x^3 + 240x$