Elective Mathematics

Question 1

1If p = 2i + 3j and q = i − j, find 2p − q.

Easy

A. 3i + 5j B. 5i + 5j C. i + 4j D. 3i + 7j

Question 2

2Find the scalar projection of a = 3i + 4j onto b = i.

Hard

A. 4 B. 3 C. 5 D. 1

Question 3

3Find the unit vector in the direction of a = 4i − 3j.

Hard

A. (0.8, −0.6) B. (1, −1) C. (4, −3) D. (0.6, −0.8)

Question 4

4Two vectors a and b are perpendicular if

Easy

A. a = b B. a · b = 1 C. a · b = 0 D. |a| = |b|

Question 5

5The position vector of the point (−2, 5) is

Easy

A. −2i + 5j B. 5i − 2j C. 2i − 5j D. −2i − 5j

Question 6

6Find |3i − 4j|.

Easy

A. 25 B. 5 C. 7 D. 1

Question 7

7If p = 3i − 2j, find |p|.

Easy

A. √13 B. 5 C. 13 D. 1

Question 8

8The points A(1, 2), B(3, 6), C(4, 8) are

Hard

A. collinear B. equidistant C. vertices of a right triangle D. vertices of a square

Question 9

9If a = 2i − j and b = 3i + 4j, find a · b.

Easy

A. 5 B. 2 C. 10 D. −2

Question 10

10Two non-zero vectors are perpendicular when

Easy

A. their sum is zero B. they are parallel C. their magnitudes are equal D. their dot product is zero