### CBSE Assignments class 09 Mathematics

Mathematics Assignments & Worksheets  For  Class IX Chapter-wise mathematics assignment for class 09. Important and useful extra questions strictly according to the CBSE syllabus and pattern with answer key CBSE Mathematics is a very good platform for the students and is contain the assignments for the students from 9 th  to 12 th  standard.  Here students can find very useful content which is very helpful to handle final examinations effectively.  For better understanding of the topic students should revise NCERT book with all examples and then start solving the chapter-wise assignments.  These assignments cover all the topics and are strictly according to the CBSE syllabus.  With the help of these assignments students can easily achieve the examination level and  can reach at the maximum height. Class 09 Mathematics    Assignment Case Study Based Questions Class IX

### Math Assignment Class XII Ch-11: 3-Dimensional Geometry

Three Dimensional Geometry
Math. Assignment Class XII Chapter 11
Important questions on Three dimensional geometry chapter 11 class XII based on the board examination point of view with answers. Revision questions based on three dimensional geometry class XII

Extra Questions of Chapter 11 Three Dimensional Geometry

 Question 1: A line makes angle 𝜶, 𝛃, 𝛾 with x-axis, y-axis, z-axis. Then find cos2𝜶, cos2𝛃, cos2𝛾 ?Ans. 1             -1 Question 2: Write vector equation of the line:  $\frac{2x-1}{\sqrt{3}} =\frac{y+2}{2} =\frac{z-3}{3}$ Question 3: Find the Cartesian equation of the line which passes through the point (-2, 4, -5) and is parallel to the line  $\frac{x+3}{3}=\frac{4-y}{5}=\frac{z+8}{6}$Hint: Two parallel lines have same direction ratio.  Ans. 3   $\frac{x+2}{3}=\frac{y-4}{-5}= \frac{z+5}{6}$ Question 4: Find angle between pair of lines $\frac{2-x}{-2}=\frac{y-1}{7}=\frac{z+3}{-3}$  and  $\frac{x+2}{-1}=\frac{2y-8}{4}=\frac{z-5}{4}$  Ans 4:   90o Question 5: Find the point on the given line at a distance 3√2 from the point (1, 2, 3).  $\frac{x+2}{3}=\frac{y+1}{2}=\frac{z-3}{2}$Ans 5:   $\lambda =0, \lambda =\frac{30}{17}$  and the point is either  $A(-2,-1,3)\; or\; A\left (\frac{56}{17},\frac{43}{17},\frac{111}{17} \right )$ Question 6: Find the length and foot of perpendicular drawn from the point (2, -1, 5) on the line  $\frac{x-11}{10}=\frac{y+2}{-4}=\frac{z+8}{-11}$Ans 6:  $\lambda =-1, Q \left ( 1,2,3 \right ), \; \; \left | PQ \right |=\sqrt{14}$ Question 7: Find the shortest distance between the lines :-  $\vec{r}=(1+\lambda)\hat{i}+(2-\lambda)\hat{j}+(\lambda +1)\hat{k}$$\vec{r}=(2\hat{i}-\hat{j}-\hat{k})+\mu (2\hat{i}+\hat{j}+2\hat{k})$Ans 7:    $\vec{b_{1}}\times \vec{b_{2}}=-3\hat{i}+3\hat{k},\; Distance\; =\frac{3\sqrt{2}}{2}$ Question 8: Find the equation of a line passing through the point P(2,-1,3) and perpendicular to the lines:$\vec{r}=(\hat{i}+\hat{j}+\hat{k})+\lambda (2\hat{i}-2\hat{j}+\hat{k})$  and $\vec{r}=(2\hat{i}-\hat{j}-3\hat{k})+\mu(\hat{i}+2\hat{j}+2\hat{k})$Ans 8:  $\vec{r}=\left ( 2\hat{i}-\hat{j}+3\hat{k} \right )+\lambda \left ( 2\hat{i}+\hat{j}-2\hat{k} \right )$ Question 9: Show that the following lines are intersecting, also find their point of intersection. $\vec{r}=3\hat{i}+2\hat{j}-4\hat{k}+\lambda(\hat{i}+2\hat{j}+2\hat{k})$$\vec{r}=5\hat{i}-2\hat{j}+\mu (3\hat{i}+2\hat{j}+6\hat{k})$ Ans 9: (-1, -6, -12) Question 10: Show that the following lines are coplanar. $\frac{5-x}{-4}=\frac{y-7}{4}=\frac{z+3}{-5}$$\frac{x-8}{7}=\frac{2y-8}{2}=\frac{z-5}{3}$ Question 11: Find the distance of the given plane from the origin: $\vec{r}.(2\hat{i}+3\hat{j}-6\hat{k})+2=0$ Ans 11 : 2/7 Question 12: Find the angle between the planes $\vec{r}.(\hat{i}-2\hat{j}-2\hat{k})=1$$\vec{r}.(3\hat{i}-6\hat{j}+2\hat{k})=0$Ans 12  $cos^{-1}\left ( \frac{11}{21} \right )$ Question 13: Find the equation of the plane which is perpendicular to the plane 5x + 3y + 6z + 8 = 0 and which contains the line of intersection of planes x + 2y + 3z - 4 = 0 and 2x + y - z + 5 = 0 Ans 13:  51x + 15y - 50z + 173 = 0 , λ = -29/7 Question 14: Find the equation of the plane passing through the point (-1, 3, 2) and perpendicular to each of the plane x + 2y + 3z = 5 and 3x + 3y + z = 0. Ans 14: 7x - 8y + 3z + 25 = 0 Question 15: Find the equation of the plane through (2, 1, -1) and (-1, 3, 4) and perpendicular to the plane    x -2y + 4z = 10. Ans 15:  18x + 17y + 4z -49 = 0 Question 16:  Find image p' of point p having position vector $\hat{i}+3\hat{j}+4\hat{k}$ in the plane  $\vec{r}.(2\hat{i}-\hat{j}+\hat{k})+3=0$ and also find |PP'|Ans. 16: Image (-3, 5, 2), Length = 2√6 Question 17: Find the distance of the point (1, -2, 3) from the plane x - y + z = 5 measured parallel to the line   $\frac{x}{2}=\frac{y}{3}=\frac{z}{-6}$Ans 17:  λ = 1/7,    AB = 1 Question 18: Find the distance of the point (-2, 3, -4) from the given line measured ∥ to the plane 4x + 12y - 3z + 1 = 0 $\frac{x+2}{3}=\frac{2y+3}{4}=\frac{3z+4}{5}$Ans 18:  λ = 2/3 , Point is (4, 5/2, 2),  Distance = 17/2 Question 19: Find the equation of the plane passing through the point P(4, 6, 2) and the point of intersection of the plane x + y - z = 8 and the line $\frac{x-1}{3}=\frac{y}{2}= \;\frac{z+1}{7}$Ans 19 $\frac{x-4}{1}=\frac{y-6}{1}=\frac{z-2}{2}$ Question 20: Find the vector equation of the plane through the line of intersection of planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x - y + z = 0. Hence find whether plane thus obtained contains the line $\frac{x+2}{5}=\frac{y-3}{4}= \;\frac{z}{5}$Ans 20 : $\vec{r}\left ( \hat{i}-\hat{k} \right )+2=0,$  Yes Question 21: Find the angle between the following line and plane : $\vec{r}=\left (\hat{i}-\hat{j}+\hat{k} \right )+\lambda (2\hat{i}-\hat{j}+3\hat{k})$ and plane  $\vec{r}.\left (2\hat{i}+\hat{j}-\hat{k} \right )=4$ Ans 21:  0o

THANKS FOR YOUR VISIT