vectors BARNES

Question 1

top number in vectors means

Answer 1

left/ right
positive = right

Question 2

The vector (3, -5) written using base vectors is

Answer 2

3i - 5j

Question 3

i is in what direction

Answer 3

the x direction

Question 4

j is in what direction

Answer 4

the y direction

Question 5

To add or subtract vectors

Answer 5

add each component separately

Question 6

To multiply by scalars

Answer 6

multiply each component by that scalar

Question 7

Parallel vector are

Answer 7

scalar multiples of each other, ie: b = ka if k is negative, the direction is reversed

Question 8

.

Answer 8

.

Question 9

If a = i + 2j, b = -3i + pj, c = -2i + 5j
Find the value of p such that b is parallel to a
Find the value of scalar k such that a + kc is parallel to 10i + 23j

Answer 9

p = -6
k = 1/32

Question 10

If v = (x,y) the magnitude is

Answer 10

IvI = l (x,y) l = square root of x^2 + y^2

Question 11

unit vector is

Answer 11

a vector with the magnitude of 1

Question 12

Unit vector in the same direction as a is

Answer 12

a^ = a / lal

Question 13

Find the angle vector
a) a = 5i + 3j makes with the i direction
b) b = 4i - 7j makes with the i direction

Answer 13

32 degrees
29.7 degrees

Question 13

.

Answer 13

.

Question 14

Position vector of point A is

Answer 14

the vector from origin O to point A
It’s written —>OA or a

Question 15

The displacement vector from point A to point B

Answer 15

—> AB
its calculated as AO + OB

Question 16

Midpoint M of line segment AB is

Answer 16

½(a + b),
where a and b are the position vectors of A and B

Question 17

Shape ABCD is a parallelogram if

Answer 17

AD = DC (implying that AD = BC so 2 pairs of parallel sides)

Question 18

Shape ABCD is a rhombus if in addition

Answer 18

magnitude of AB = magnitude of DC

Question 19

Points A, B, and C are collinear if

Answer 19

they lie on a straight line
To prove: show AB is // to BC, then state B is a common point
BC = k AB

Question 20

The vertices of a quadrilateral PQRS have coordinates P(-2, 1), Q(5, -3),
R(6, 0) and S(-1, 5).
The midpoints of sides PQ, QR, RS and SP are A, B, C and D.
Prove that ABCD is a parallelogram.

Answer 20

AB = DC = (4, -0.5)

Question 21

Three points are A(-3, 2), B(6, 5) and C(12, 7)
Show that A, B and C lie on a straight line

Answer 21

AB = 3/2 BC

Question 22

Determine whether the points A(4, 2a), B(1, 2a+1) and C(7, 2a-1) are collinear

Answer 22

AB = -2 BC