Phys351-HW1

# Phys351-HW1 - Vector algebra 101 1 1.1 Given two position...

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Vector algebra 101 1. 1.1 – Given two position vectors ~ r A = - ˆ e 1 - 3 ˆ e 2 - 4 ˆ e 3 and ~ r B = 2 ˆ e 1 + 2 ˆ e 2 + 2 ˆ e 3 , ﬁnd the unit vector ˆ e AB that points from point A to point B . 2. The scalar component of a vector ~ A along a vector ~ B is given by ~ A · ± ~ B k ~ B k ~ A · ˆ e B . 3. The vector component of a vector ~ A along a vector ~ B is given by ± ~ A · ˆ e B ˆ e B is a vector. 4. 1.3 – Given ~ r A = 2ˆ e 1 + 5 ˆ e 2 - ˆ e 3 , ~ r B = 3 ˆ e 1 - 2 ˆ e 2 + 4 ˆ e 3 , and ~ r C = - 2 ˆ e 1 - 2 ˆ e 2 + 4 ˆ e 3 , Find the angle between vectors ~ r AB and ~ r AC . Hint: cos θ = ~ A · ~ B | ~ A || ~ B | or sin θ = ~ A × ~ B | ~ A || ~ B | . 5. 1.12 – Given two position vectors ~ r A = 2 ˆ e 1 +5 ˆ e 2 - 3 ˆ e 3 and ~ r B = - 3 ˆ e 1 + ˆ e 2 + 4 ˆ e 3 , ﬁnd (a) their separation; (b) the distance from the origin to the midpoint of AB; (c) ﬁnd the unit vector ˆ e AB that points from point A to point B ; (d) the point of intersection of the line AB with the ( x = 0) plane.

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6. 1.25 – Given ~ r A = 6ˆ e 1 + 2 ˆ
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## This note was uploaded on 01/28/2010 for the course PHYS 351 taught by Professor Gangopashyaya during the Spring '09 term at Loyola Chicago.

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Phys351-HW1 - Vector algebra 101 1 1.1 Given two position...

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