mechanics help needed! vectors, components, magnitudes etc
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
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:
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
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 ! ! !