Write the direction consines of the line whose cartesian equation… - Vidyadip

Question

Write the direction consines of the line whose cartesian equations are 2x = 3y = -z.

✓

Answer

We have2x = 3y = -z
The equation of the given line can be re-written as
$\frac{\text{x}}{\frac{1}{2}}=\frac{\text{y}}{\frac{1}{3}}=\frac{\text{z}}{-1}$
$\frac{\text{x}}{3}=\frac{\text{y}}{2}=\frac{\text{z}}{-6}$
The diraction ratios of the line parallel to AB are proportional to 3, 2, -6.
Hence, the direction cosines of the line parallel to AB are proportional to
$\frac{3}{\sqrt{3^2+2^2+(-6)^2}},\frac{2}{\sqrt{3^2+2^2+(-6)^2}},\frac{-6}{\sqrt{3^2+2^2+(-6)^2}}$
$=\frac{3}{7},\frac{2}{7},-\frac{6}{7}$

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 Questions" from Three Dimensional Geometry→Three Dimensional Geometry — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $A$ is a square matrix of order $3$ such that $adj\ (2A) = k\ adj\ (A),$ then write the value of $k$.

What is the principal value of $\sin^{-1}\Big(-\frac{\sqrt3}{2}\Big)$

A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is ₹ 100 and that on a bracelet is ₹ 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit? It is being given that at least one of each must be produced.

Write a 2×2 matrix which is both symmetric and skew-symmetric.

If $A$ is a square matrix of order $3$ such that $|$adj $A| = 64,$ find $|A|.$

If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then write the values of $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}$.

Evaluate the following integrals:
$\int\limits^{2}_0\text{x}[\text{x}]\text{dx}$

Evaluate the following integrals:
$\int\bigg (2^{\text{x}}+\frac{5}{\text{x}}-\frac{1}{\text{x}^{\frac{1}{3}}}\bigg)\text{dx}$

If x and y are connected parametrically by the equation $x = \cos \theta - \cos 2\theta ,y = \sin \theta - \sin 2\theta $, without eliminating the parameter, find $\frac{{dy}}{{dx}}.$

Check the injectivity and surjectivity of the below function:
$f : Z \rightarrow Z$ given by $f(x) = x^2$