The CBSE Class 12th Mathematics Examination 2020 will be held on March 17, 2020. The students appearing in the CBSE Class 12th Mathematics Board Examination 2020 can go through the below-mentioned questions for Chapter 11 - Three Dimensional Geometry. These Questions are based on the latest syllabus prescribed by the CBSE Board.
Question 1- Find the foot of the perpendicular from the point (2, 3, -8) to the given line. Also, find the perpendicular distance from the given point to the line.
Answer: The foot of the perpendicular is (2, 6, -2) and the perpendicular distance is 3√5 units.
Question 2- Find the length and the foot of the perpendicular from the point to the given plane: 2x - 2y + 4z + 5 = 0.
Answer: The foot of the perpendicular is (0, 5/2, 0) and the perpendicular distance is √6 units.
Question 3- Find the equation of the line which passes through the point (3, 0, 1) and is parallel to the planes x + 2y = 0 and 3y - z = 0.
Answer: The equation will be:
Question 4- Find the shortest distance between the given lines:
Answer: 14 units.
Question 5- Find the equation of the plane which is perpendicular to the plane 5x + 3y + 6z + 8 = 0 and contains the Line of intersection of the planes x + 2y + 3z - 4 = 0 and 2x + y - z+ 5 = 0.
Answer: The equation of the plane: 51x + 15y - 50z + 173 = 0.
Question 6- Show that the straight lines whose direction cosines are given by 2l + 2m - n = 0 and mn + nl + lm = 0 are at right angles.
Answer: θ = π/2
Question 7- Show that the lines given below are coplanar:
Answer: The first and second columns are identical. Hence, the given lines are coplanar.
Answer: The given lines intersect at (-1, -1, -1).
Question 10- Find the angle between the below-mentioned lines:
Answer: θ = cos-1 19/21
The above-mentioned questions are strictly based on the latest CBSE pattern prescribed by the CBSE Board. The students appearing for the CBSE Class 12th Mathematics Examination 2020 will find these questions helpful for the last minute preparation for the upcoming Examination.