Using direction ratios show that the points A(2, 3, -4) B(1, - 2,… - Vidyadip

Question

Using direction ratios show that the points A(2, 3, -4) B(1, - 2, 3) and C(3, 8, -11) are collinear.

✓

Answer

Here A(2, 3, -4), B(1, -2, 3) and C(3, 8, -11).
Direction ratios of AB = (1 - 2, -2 - 3, 3 + 4) = (-1, -5, 7)
Direction ratios of BC = (3 - 1, 8 + 2, -11 - 3) = (2, 10, -14)
Here, the respective direction consines of AB and AC,
$\frac{-1}{2}=\frac{-5}{10}=\frac{7}{-14}$ are proportional.
Also, Bis the common point between the two lines,
$\therefore$ The points A(2, 3, -4) B(1, -2, 3) and C(3, 8, -11) are collinear.

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 "4 Marks" from Direction Cosines and Direction Ratios→Direction Cosines and Direction Ratios — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Solve the following differential equation:
$2\text{xy dx}+(\text{x}^2+2\text{y}^2)\text{dy}=0$

Evaluate the following integrals:

$\int\frac{1}{\sqrt{7-3\text{x}-2\text{x}^2}}\text{ dx}$

Evaluate the following integrals as limit of sum:
$\int\limits^3_0(\text{x}+4)\text{dx}$

Find the equation of the passing throught the point (1, 2, 1) and perpendicular to the joining the point (1, 4, 2) and (2, 3, 5). Find also the perpendicular distance of the origin from this plane.

Solve the following differential equation:
$\frac{\text{dy}}{\text{dx}} = (\text{x}+\text{y})^2$

Differentiate the following functions with respect to x:
$\tan^{-1}\Big(\frac{4\text{x}}{1-4\text{x}^2}\Big),-\frac{1}{2}<\text{x}<\frac{1}{2}$

If xy² = 1, prove that $2\frac{\text{dy}}{\text{dx}}+\text{y}^3=0$

Find the value of $\lambda$ such that the line $\frac{\text{x}-2}{6}=\frac{\text{y}-1}{\lambda}=\frac{\text{z}+5}{-4}$ is perpendicular to the plane 3x - y - 2z = 7.

A diet for a sick person must contain at least 4000 units of vitamins, 50 units of minerals and 1400 units of calories. Two foods A and B are available at a cost of Rs. 5 and Rs. 4 per unit respectively. One unit of the food A contains 200 units of vitamins, 1 unit of minerals and 40 units of calories, while one unit of the food B contains 100 units of vitamins, 2 units of minerals and 40 units of calories. Find what combination of the foods A and B should be used to have least cost, but it must satisfy the requirements of the sick person. Form the question as LPP and solve it graphically.

Draw a rough sketch of the region {(x, y) : y² < 3x, 3x² + < 16} and find the area by the region using mwthod of integration.