# B.A Additional Mathematics 1st year for Vector Calculus

## BACHELOR OF ARTS ADDITIONAL (MATHEMATICS), YEAR-1

VECTOR CALCULUS

Time: 3 hours                                                                                                  M.Marks:60

Note: – Attempt any 5 questions.

All questions carry equal marks.

Q.1      (i): Find the position vector of a point A such that is inclined to OX at 60 and to OY at at 45 and OA 10 units. OA ????

(ii): Find a unit vector in the direction of _ _ 3 2 6 a i j k ?????_.

Q.2      (i): Find the value of ‘?’ for which ?(î + ? + k ) is a unit vector.

(ii): If is a vector of magnitode 5 pointing eastwards and b is a vector pointing westward of magnitude 10 .What is the magnitude and direction of the vector a b?

Q.3      _ _ _ _ _ _ Show that the vectors If 3 2 and 2 4 4 , 3 2 1 are linearly independent. a i j k b i j k c i j k ?????????????????_ _ __ _ _

Q.5      ?????Vector Algebra Assignment/Worksheet For solutions write to us at

For more assignments/worksheets/Solved examples in Physics, Chem and Math visit us at Ifa , b, c are the position vectors of the vertices A, B, C of a ??ABC respectively. Find an expression for the area of ??ABC and hence deduce the condition for the points A, B, C to be collinear.

Q.6      Find the components and magnitude of the vector PQ ? , where P(-1,-2,4) and Q(2,0,-2).

Q.7      Find if the vectors 3 and 4 5 2 are perpendicular to each other. a i j k b i j k ???

??????????????? ?????????

Q.8      (i): For what values of ‘?’, are the vectors (2î – 3 ? ) and (?i – 6?) parallel

(ii): Find the area of a triangle having the points A (1, 1, 1), B (1, 2, 3) and C (2, 3, 1) as its vertices.

Q.9      If, are three vectors, such that 3, 4, 5. Each of the three vectors is perpendicular to the sum of the other two vectors. Find the value of .a b c a b c.

Note: Above sample paper of B.A Additional Mathematics 1st year for Vector Calculus has been prepared after reviewing various sample papers from various universities. We are not sure whether your university has same or similar question patterns. We are just trying to help you by providing the possibilities. We always suggest you to go thoroughly your textbooks, teacher’s notes and the syllabus for better preparation for your coming examination.

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