(a) Express the vector ~A= (Ax,Ay) = (−5 m,−2 m) using unit vectors ˆı and ˆ|.
Also express ~A in magnitude and direction form (|~A |, ), where the angle is measured
with respect to the positive x-axis, anticlockwise angles being positive.
(b) An acceleration vector of magnitude 9.81 m/s2 makes an angle of 75 with the positive
z-axis. Find the scalar components of the vector parallel to and perpendicular to the zaxis.
You now rotate the z-axis until the scalar acceleration component parallel to the
z-axis changes sign, becoming equal to the negative of its previous value. What now is the
angle between the vector and the z-axis?
(c) When vector ~C is subtracted from vector ~D , the resulting vector is equal to twice the
sum of the two vectors. Write this condition as a statement in vector algebra involving
~Cand ~D
. Show that this requires that ~D is a scalar multiple of ~C. Find the ratio of
the magnitudes of the two vectors, and the angle between them. Draw a diagram to show
their relationship.
2006-10-02
18:22:18
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2 answers
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asked by
behshad c
1