(a - b) middot c + b middot (c + a). a middot (a + 2c) + (2b - a) middot (a + 2c

Question

(a - b) middot c + b middot (c + a). a middot (a + 2c) + (2b - a) middot (a + 2c) - 2b middot (a + 2c). Taking a = 2i + j, b = 3i - j + 2k, c = 4i + 3k, calculate: the three dot products a middot b, a middot c, b middot c; the cosines of the angles between these vectors; the component of a (i) in the b direction, (ii) in the c direction; the projection of a (i) in the b direction, (ii) in the c direction. Repeat Exercise 11 with a = j + 3k, b = 2i - j + 2k, c = 3i - k. Find the unit vector with direction angles 1/3pi, 1/4pi, 2/3pi,

Explanation / Answer

b.)

for vector a= 2i+j

= cos a = 2 / 5

= cos b = 1 / 5

= cos c = 0

for vector b = 3i-j+2k

= cos a = 3 / 14

= cos b = -1 / 14

= cos c = 2/ 14

for vector b = 4i+3k

= cos a = 4 / 5

= cos b = 0

= cos c =  3 / 5

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