Download App

Introduction to 3D coordinate geometry — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSIntroduction to 3D coordinate geometry4 Marks
Question
Planes are drawn through the points (5, 0, 2) and (3, -2, 5) parallel to the coordinate planes. Find the lengths of the edges of the rectangular parallelopiped so formed.
✓

Answer

IMAGE
Clearly, PBEC and QDAF are the planes parallel to the yz-plane such that their distances from the yz-plane are 5 and 3, respectively.
$\therefore$ PA = Distance between planes PBEC and QDAF
= 5 - 3
= 2
PB is the distance between planes PAFC and BDQE that are parallel to the zx-plane and are at distances 0 and -2, respectively, from the zx-plane.
$\therefore$ PB = 0 - (-2)
= 2
PC is the distance between parallel planes PBDA and CEQF that are at distances 2 and 5, respectively, from the xy-plane.
$\therefore$ PC = 2 - 5
= -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 "(Each question 4 marks)" from Introduction to 3D coordinate geometry→Introduction to 3D coordinate geometry — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

In a large metropolitan area, the probabilities are 0.87, 0.36, 0.30 that a family (randomly chosen for a sample survey) owns a colour television set, a black and white television set, or both kinds of sets. What is the probability that a family owns either any one or both kinds of sets?
→
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow\frac{3\pi}{2}}\frac{1+\text{cosec}^3\text{x}}{\cot^2\text{x}}$
→
Prove the following by the principle of mathematical induction: $1 + 2 + 3 + ... + \text{n}=\frac{\text{n}(\text{n}+1)}{2}$ i.e, the sum of the first n natural numbers is $\frac{\text{n}(\text{n}+1)}{2}.$
→
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\sqrt{1+\text{x}}-1}{\text{x}}$
→
Find the mean, and standard deviation for the following data:
Marks:
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Frequency:
1
6
6
8
8
2
2
3
0
2
1
0
0
0
1
→
For any two sets of A and B, prove that:

$\text{B}'\subset\text{A}'\Rightarrow\text{A}\subset\text{B.}$

→
Find the general solution for each of the following equations: $\cos4\text{x}=\cos2\text{x}$
→
In each of the followin find the equation of the hyperbola satisying the given conditions: foci $(\pm5, 0)$, transverse axis = 8 [NCERT]
→
Let r and n be positive integers such that 1 < r < n. Then prove the following: ${^\text{n}\text{C}}_{\text{r}}+2\ {^\text{n}\text{C}}_{\text{r}-1}+{^\text{n}\text{C}}_{\text{r}-2}={^\text{n+2}\text{C}}_{\text{r}}$
→
Prove that: $4\cos\text{x}\cos\Big(\frac{\pi}{3}+\text{x}\Big)\cos\Big({\frac{\pi}{3}-\text{x}}\Big)=\cos3\text{x}$
→