Question:
Find the intercepts cut off by the plane 2x+y-z = 5
Find the intercepts cut off by the plane 2x+y-z = 5
Updated On: Sep 20, 2023
Hide Solution
Verified By Collegedunia
Solution and Explanation
2x+y-z=5...(1)
Dividing both sides of equation(1) by 5, we obtain
\(\frac{2}{5}x+\frac{y}{5}-\frac{z}{5}=1\)
\(\Rightarrow \frac{x}{\frac{5}{2}}+\frac{y}{5}+\frac{z}{-5}=1\)...(2)
It is known that the equation of a plane in intercept form is \(\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\), where a,b,c are the intercepts cut off by the planet at x, y, and z axes respectively.
Therefore, for the given equation, a=\(\frac{5}{2}\), b=5, and c=-5
Thus, the intercepts cut off by the plane are \(\frac{5}{2}\), 5, and -5.
Was this answer helpful?
0
0
Top Questions on Three Dimensional Geometry
- If A(2,1,-1), B(6,-3,2), C(-3,12,4) are the vertices of a triangle ABC and the equation of the plane containing the triangle ABC is $53x+by+cz+d=0$, then $\frac{d}{b+c}=$
- TS EAMCET - 2025
- Mathematics
- Three Dimensional Geometry
- If $(\alpha, \beta, \gamma)$ is the foot of the perpendicular drawn from a point $(-1,2,-1)$ to the line joining the points $(2,-1,1)$ and $(1,1,-2)$, then $\alpha+\beta+\gamma=$
- TS EAMCET - 2025
- Mathematics
- Three Dimensional Geometry
- If m:n is the ratio in which the point $\left(\frac{8}{5}, \frac{1}{5}, \frac{8}{5}\right)$ divides the line segment joining the points (2,p,2) and (p,-2,p) where p is an integer then $\frac{3m+n}{3n}=$
- TS EAMCET - 2025
- Mathematics
- Three Dimensional Geometry
- Let $\pi_1$ be the plane determined by the vectors $\hat{i}+\hat{j}, \hat{i}+\hat{k}$ and $\pi_2$ be the plane determined by the vectors $\hat{j}-\hat{k}, \hat{k}-\hat{i}$. Let $\vec{a}$ be a non-zero vector parallel to the line of intersection of the planes $\pi_1$ and $\pi_2$. If $\vec{b} = \hat{i}+\hat{j}-\hat{k}$ then the angle between the vectors $\vec{a}$ and $\vec{b}$ is
- TS EAMCET - 2025
- Mathematics
- Three Dimensional Geometry
Show that the following lines intersect. Also, find their point of intersection:
Line 1: \[ \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4} \]
Line 2: \[ \frac{x - 4}{5} = \frac{y - 1}{2} = z \]
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Mathematics
- Three Dimensional Geometry
View More Questions
Questions Asked in CBSE CLASS XII exam
- Emily, Flora and Ginni entered into a partnership on 1st October, 2023 with capitals of ₹ 10,00,000 each. The partnership deed provided for interest on capital at 10% p.a. The firm earned a net profit of ₹ 7,50,000 for the year ended 31st March, 2024. The amount of profit transferred to Emily’s capital account was :
- CBSE CLASS XII - 2025
- Partnership Accounts
- "The Government had launched Incredible India Campaign to promote tourism in various parts of the country."
Elaborate the impact of Incredible India Campaign on foreign exchange reserves and Balance of Payment of India.- CBSE CLASS XII - 2025
- Balance of payments (BOP)
- Ajanta Ltd. purchased machinery worth Rs 36,00,000 from Sujata Ltd. Ajanta Ltd. paid half the amount to Sujata Ltd. through a bank draft and the balance by issuing 8 debentures of Rs 100 each at a discount of 10.
Pass the necessary journal entries in the books of Ajanta Ltd. for the above transactions.- CBSE CLASS XII - 2025
- Debentures
- From the following information obtained from the books of KVK Ltd., calculate Net Assets Turnover Ratio and Debt Equity Ratio:
Information Table
Information Amount (₹) Preference Share Capital 8,00,000 Equity Share Capital 12,00,000 General Reserve 2,00,000 Balance in Statement of Profit and Loss 6,00,000 15% Debentures 4,00,000 12% Loan 4,00,000 Revenue from Operations 72,00,000 - CBSE CLASS XII - 2025
- Financial Statement Analysis
- Zaina, Yash and Kiran were partners in a firm sharing profits and losses in the ratio of 2 : 2 : 1. Zaina died on 1st July, 2024. As per the partnership deed, Zaina’s share of profit or loss till the date of her death was to be calculated on the basis of sales. Sales for the year ended 31st March, 2024 amounted to ₹ 4,00,000 and that from 1st April to 30th June, 2024 was ₹ 1,50,000. The profit for the year ending 31st March, 2024 was ₹ 1,00,000. Calculate Zaina’s share of profit in the firm till the date of her death and pass necessary journal entry for the same.
- CBSE CLASS XII - 2025
- Retirement and Death of a Partner
View More Questions
Concepts Used:
Plane
A surface comprising all the straight lines that join any two points lying on it is called a plane in geometry. A plane is defined through any of the following uniquely:
- Using three non-collinear points
- Using a point and a line not on that line
- Using two distinct intersecting lines
- Using two separate parallel lines
Properties of a Plane:
- In a three-dimensional space, if there are two different planes than they are either parallel to each other or intersecting in a line.
- A line could be parallel to a plane, intersects the plane at a single point or is existing in the plane.
- If there are two different lines that are perpendicular to the same plane then they must be parallel to each other.
- If there are two separate planes which are perpendicular to the same line then they must be parallel to each other.