Download App

Straight line in space — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSStraight line in space3 Marks
Question
A line passes throuth the point with position vector $2\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}$ and is in the direction of $3\hat{\text{i}}+4\hat{\text{j}}-5\hat{\text{k}}.$ Find equations of the line in vector and cartesian form.
✓

Answer

We know that the vector equation of a line passing through a point with position vector $\vec{\text{a}}$ and parallel to the vector $\vec{\text{b}}$ is $\vec{\text{r}}=\vec{\text{a}}+\lambda\vec{\text{b}}.$
Here,
$\vec{\text{a}}=2\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}$
$\vec{\text{b}}=3\hat{\text{i}}+4\hat{\text{j}}-5\hat{\text{k}}$
So, the vector equation of the required line is
$\vec{\text{r}}=\big(2\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}\big)+\lambda\big(3\hat{\text{i}}+4\hat{\text{j}}-5\hat{\text{k}}\big)$
Here, $\lambda$ is a parameter.

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 "3 Marks Question" from Straight line in space→Straight line in space — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate the following integrals:$\int\frac{\text{x}+7}{3\text{x}^2+25\text{x}+28}\text{ dx}$
→
Find $\frac{d y}{d x}$, if $y =\sqrt{\frac{(x-1)(x-2)}{(x-3)(x-4)(x-5)}}$.
→
Solve the following differential equations:$2\text{x}\frac{\text{dy}}{\text{dx}}=5\text{y},\text{y}(1)=1$
→
For $A, B$ and $C$ the chances of being selected as the manager of a firm are in the ratio $4:1:2$ respectively. The respective probabilities for them to introduce a radical change in marketing strategy are $0.3, 0.8$ and $0.5$. If the change does take place, find the probability that it is due to the appointment of $B$ or $C$
→
Prove that $\int_a^b f(a+b-x) d x=\int_a^b f(x) d x$ and using it find $\int_4^9 \frac{f(x)}{f(x)+f(13-x)} d x$.
→
Find the mean and standard deviation of the following probability distributions$:$
$x_i$ $0$ $1$ $3$ $5$
$p_i$ $0.2$ $0.5$ $0.2$ $0.1$
→
If $\vec{\text{a}}\times\vec{\text{b}}=\vec{\text{b}}\times\vec{\text{c}}\neq0,$ then show that $\vec{\text{a}}+\vec{\text{c}}=\text{m}\vec{\text{b}},$ where m is any scalar.
→
Let $f$ be an invertible real function. Write $(f^{-1}$ of $)(1) + (f^{-1}$ of $)(2) + ..... + (f^{-1}$of$)(100).$
→
An unbiased coin is tossed. If the result is a head, a pair of unbiased dice is rolled and the sum of the numbers obtained is noted. If the result is a tail, a card from a well shuffled pack of eleven cards numbered $2, 3, 4, ....., 12$ is picked and the number on the card is noted. What is the probability that the noted number is either $7$ or $8$?
→
Evaluate the integral: $\int_0^\pi \frac{x}{a^2 \cos ^2 x+b^2 \sin ^2 x} d x$
→