mechanics help needed! vectors, components, magnitudes etc

**QUESTION ONE:**

i and j represent vectors.

Given that a= i-2j and b= -3i , find:

(a) λ, if a + λb is parallel to -i-3j

(b) μ, if μa + b is parallel to 2i + j

**QUESTION 2:**

http://img221.imageshack.us/img221/2289/maths6uw.jpg

The vector **a** is in the plane of the coordinate axes *0x* and *0y* as in the above diagram. Find the components of **a** along *0x* and *0y* when **a** equals:

a) 2

b) 3

c) 6

d) 10

**QUESTION THREE:**

The vector **a ** is in the plane of the coordinate axes *0x* and *0y* as in the previous question, but makes an angle with the positive direction *0x*. Find the components of **a** along *0x* and *0y* when **a**=10 and the angle equals:

a) 60 degrees

b) 120 degrees

c) 150 degrees

d) 240 degrees

e) 300 degrees

**QUESTION FOUR:**

Vectors a and b are in the plane of the coordinate axes 0x and 0y, a makes an angle "alpha" with 0x, b makes an angle "beta" with 0x. Find:

a) the components of a and b along 0x, 0y

b) the sum of these components along 0x, 0y

c) the magnitude of a + b

in each of the following places.

i) a=3, b=4, alpha=0, beta=90 degrees

ii) a=3, b=4, alpha=0, beta= 60 degrees

iii) a=3, b=4, alpha=30 degrees, beta= 60 degrees

iv) a=5, b=8, alpha=30 degrees, beta=60 degrees

v) a=5, b=8, alpha=30 degrees. beta=150 degrees

ANY HELP ON ANY OF THESE QUESTIONS WOULD BE GREATLY APPRECIATED.

FAIRLY SIMPLE EXPLANATIONS WOULD ALSO BE FABULOUS ! ! !

THANKSSSS

EMY.

XXX