If a line has direction ratios 2, -1, -2, determine its direction… - Vidyadip

Question

If a line has direction ratios 2, -1, -2, determine its direction cosines.

✓

Answer

Let the direction cosines of a line be l, m and n.

Now,

$\text{l}=\frac{2}{\sqrt{2^2+(-1)^2+(-2)^2}}=\frac{2}{3}$

$\text{m}=\frac{-1}{\sqrt{2^2+(-1)^2+(-2)^2}}=\frac{-1}{3}$

$\text{n}=\frac{-2}{\sqrt{2^2+(-1)^2+(-2)^2}}=\frac{-2}{3}$

$\therefore$ The direction consines of the line are $\frac{2}{3},\frac{-1}{3},\frac{-2}{3}.$

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 "2 Marks" from Three Dimensional Geometry→Three Dimensional Geometry — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

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

Evaluate the following integrals:

$\int\frac{\cos\text{x}}{\sqrt{4-\sin^2\text{x}}}\text{ dx}$

The equations of a line are given by $\frac{4-\text{x}}{3}=\frac{\text{y}+3}{3}=\frac{\text{z}+2}{6}.$ Write the direction cosines of a line parallel to this line.

Solve the equation for $\mathrm{x}, \mathrm{y}, \mathrm{z}$ and $\mathrm{t}$ if $2\left[\begin{array}{ll}x & z \\ y & t\end{array}\right]+3\left[\begin{array}{cc}1 & -1 \\ 0 & 2\end{array}\right]=3\left[\begin{array}{cc}3 & 5 \\ 4 & 6\end{array}\right]$.

Find the domain of the following function:

$\text{f(x)}=\sin^{-1}\sqrt{\text{x}^2-1}$

Determine whether or not the definition of * given below gives a binary operation. In the event that * is not a binary operation give justification of this.
On R, define by a * b = ab².
Here, Z⁺ denotes the set of all non-negative integers.

Write the minimum value of $\text{f}(\text{x})=\text{x}+\frac{1}{\text{x}},\text{x}>0.$

Let $\text{f}:\Big(-\frac{\pi}{2},\frac{\pi}{2}\Big)\rightarrow\ \text{R}$ be a function defined by f(x) = cos[x]. write range (f).

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are unit vectors, then write the value of $\big|\vec{\text{a}}\times\vec{\text{b}}\big|^2+\big(\vec{\text{a}}.\vec{\text{b}}\big)^2.$

State whether $\text{f}(\text{x})=\tan\text{x}-\text{x}$ is increasing or decreasing its domain.