Thread: experts needed! please! mechanics!

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:



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

1. Two plane vectors ai + bj and ci + dj are in the same direction the the ratios a:b and c:d are equal. Here a+lb is (1-3l)i - 2j and this is parallel to -i-3j if the ratios (1-3l):-2 and -1:-3 are equal: that is, cross-multiplying, if (1-3l)(-3) = (-1)(-2). So 1-3l = -2/3, l = 5/9.

ok but

the textbook answer for part (a) is -0.5
and part (b) is 1

hmmm

xx

Try the book answer for yourself: (i-2j) - 0.5(-3i) = 2.5i - 2j. This isn't parallel to -i-3j.