1. This document provides 15 mathematics assignment questions related to vectors and 3D geometry for a senior secondary course. 2. Students are instructed to show their work on separate paper, include their details, get the assignment checked by their teacher, and not send it directly to the exam board. 3. The questions cover topics like interpreting vector expressions, finding position and unit vectors, determining if points are collinear, using vectors to prove properties of triangles, finding positions of points that divide line segments internally or externally, finding equations of lines and planes, finding angles between lines and planes, determining perpendicular lines, and finding equations and properties of spheres.

1. SENIOR SECONDARY COURSE
MATHEMATICS
Student’s Assignment - 6C
Maximum Marks : 50 1
Time : 1 --- Hours
2
INSTRUCTIONS :
Answer all the questions on a separate sheet of paper
Give the following information on your answer sheet :
Name
Enrolment number
Subject
Assignment number
Address
Get your assignment checked by the subject teacher at your study centre
so that you get positive feedback about your performance.
Do not send your assignment to National Institute of Open Schooling
→
1. If a = 4 , interperet each of the following
→ →
(i) 4 a (ii) –7a (2)
→ ∧ ∧ ∧
2. Find the position vector of the point B if AB = 2i + j – 3k and the
∧ ∧ ∧
position vector of the point A = i + 2j – k (2)
→ → → ∧ ∧ ∧
3. Find a unit vector in the direction of r – s if r = 3i + 2j – 4k and
∧
→ ∧ ∧
s = i + j – 2k (2)
∧ ∧ ∧ ∧ ∧ ∧
4. Find the value of "a" such that the points 10i + 3j , 12 i – 5j and ai + 11j
are collinear (3)
5. Using vector, prove that the line segment joining the mid-points of two
sides of a triangle is parallel to the third side and is half of it. (3)
6. Find the position vector of the point which divides the join of the points with
→ → → →
position vectors 2a – 3b and 3a – 2b in the ratio 2:3 internally. (3)
7. If vertices A and B of a triangle ABC are the points (2, –4, 3) and
(3, –1, –2) respectively, find the vertex C if it is given that the centroid of
the triangle is the point (1, 0, 3) . (2)

2. Student’s Assignment - 6C :: 91
8. Find the equations of the line passing through the points (1, 2, –1) and
(3, –1, 2). Also give its direction cosines. (3)
9. Find the equation of the plane through the point (–1, 0, 7) and parallel to
the plane 3x –5y + 4z = 11 (3)
10. Find the angle between the line
x– 2 y+ 1 z– 3
−−−− = −−−− = −−−− and the plane 3x + 4y + z + 5 = 0
−3−
− −−−
–1
−−−
2 (4)
11. For what value of p will the line through the point (4, 1, 2) and (5, p, 0)
be perpendicular to the line through the points (2,1,1) and (3,3, –1) ? (4)
12. Find the projection of the line segment joining the points (5, 2, –1) and
(7, 3, 2) on the line joining the points (–2, 3, 2) and (3, 5, 4). (4)
13. If a plane makes intercepts a, b and c with X – axis, Y - axis and Z - axis
respectively, show that the equation of the plane is
x y z
−−− + −−− + −−− = 1 (5)
a b c
14. Show that the lines 2 x = 3y = –z and 6x = –y = –4z are
perpendicular to each other. (5)
15. Find the equation of the sphere through the points (1, 2, 3), (0, –2, 4),
(4, –4, 2 ) and (3, 1, 4). Find its radius and centre. (5)