It is only through constant practice and dedication that a student can crack it. A path 5 m wide is to be built outside and around it. The cost of 1m 2 land is Rs. Visit to main page or of the page. In these situations, the student is forced to spend additional time on researching other topics to solve one sum. Find the area of the path. Q3 : Find the Cartesian equation of the following planes: a b c Answer : a It is given that equation of the plane is For any arbitrary point P x, y, z on the plane, position vector is given by, Substituting the value of in equation 1 , we obtain This is the Cartesian equation of the plane.
Find the circumference of the inner and the outer circles, shown in the adjoining figure. Finding other metrics such as breadth and area along with the perimeter are some of the different metrics that can be found. Referring to these solutions would help the student understand their mistake and make them cautious not to repeat it again. The perimeter of a rectangle is 130 cm. Therefore, the direction cosines of the normal to the plane are and the distance of normal from the origin is units. Q5 : Find the equation of the line in vector and in Cartesian form that passes through the point with position vector and is in the direction. These solutions provide a proper guidance and thorough learning experience.
The angle between them is given by, b The equations of the planes are and Here, and Thus, the given planes are perpendicular to each other. We will do the next level of statistics in chapter than whatever we have studied in classes 8, 9 and 10. Learning to solve difficult problems helps students to open their minds to new ways of approaching the problem. Q17 : Find the shortest distance between the lines whose vector equations are Answer : The given lines are Exercise 11. Answer : The given lines are It is known that the shortest distance between two lines, , is given by Comparing to equations 1 and 2 , we obtain Substituting all the values in equation 1 , we obtain Therefore, the shortest distance between the two given lines is 9 units. Solution: Chapter 11 Perimeter and Area Exercise 11.
Solving various problem sets along with a host of different examples is important to understand the major types of problems along with figuring out the different metrics such as Perimeter and Area. Q15 : Find the shortest distance between the lines and Answer : The given lines are and It is known that the shortest distance between the two lines, , is given by, Comparing the given equations, we obtain Substituting all the values in equation 1 , we obtain Since distance is always non-negative, the distance between the given lines is units. This chapter will take the students through the wonderful world of Perimeter and Area. Q14 : If the points 1, 1, p and — 3, 0, 1 be equidistant from the plane , then find the value of p. The length of the wall is 4. The students can go through chapter wise solutions from the table provided below.
Solution: Let the breadth of the rectangular plot of land be b. Q4 : Find the equation of the line which passes through the point 1, 2, 3 and is parallel to the vector. The diameter of the flower bed is 66 m. Students have the luxury to customize their learning experience by studying each topic at their own pace without worrying about deadlines or without rushing. Whenever we compare two quantities, they are more likely to be unequal than equal. For other solutions, please visit to or or or go for Solutions.
The solutions have been worked out by some of the best teachers in the country, who have a thorough knowledge of the subject and are part of the Vedantu faculty. Q7 : Find the vector equation of the plane passing through 1, 2, 3 and perpendicular to the plane Answer : The position vector of the point 1, 2, 3 is The direction ratios of the normal to the plane, , are 1, 2, and — 5 and the normal vector is The equation of a line passing through a point and perpendicular to the given plane is given by, Q8 : Find the equation of the plane passing through a, b, c and parallel to the plane Answer : Any plane parallel to the plane, , is of the form The plane passes through the point a, b, c. Thus, these are some of the different solutions for class 7. Answer : The equations of the given planes are and It is known that if and are normal to the planes, and , then the angle between them, Q, is given by, Here, Substituting the value of , in equation 1 , we obtain Q13 : In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them. Using these solutions can be a good move towards refining maths fluency and achieve greater success. Just follow them and start learning process.
Therefore, the coordinates of the foot of the perpendicular are b Let the coordinates of the foot of perpendicular P from the origin to the plane be x1, y1, z1. Find a the area of the land b the price of the land, If the land is of rectangular shape measuring 300 m in length and 400 m in breadth. Answer : It is given that the line passes through the point with position vector It is known that a line through a point with position vector and parallel to is given by the equation, This is the required equation of the line in vector form. Also find the area of the park excluding cross roads. Combinations — The number of ways of selecting r things out of n different things is called r combination number of n things. A door of length 2 m and breadth 1 m is fitted in a wall. Find the area of the path.
Q6 : If the lines and are perpendicular, find the value of k. Answer : It is given that the line passes through the point A 1, 2, 3. For other solutions, please visit to or or or go for Solutions. Maths is a lot like learning to tie a shoelace. Answer : a The position vector of point 1, 0, — 2 is The normal vector perpendicular to the plane is The vector equation of the plane is given by, is the position vector of any point P x, y, z in the plane. Hence, the correct answer is B. Find the area of each of the following triangles : Solution: Question 3.