Given vectors a-1; 1; 1, b 0; 2; – 2, c -3; 2; 0 and d-2; 1; – 2 Find the coordinates of vectors: a) 3a+2b-c, b) – a+2c-d
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a) The coordinates of vector 3a+2b-c are (0,9,-2).
We can calculate this by using the following formula:
3a+2b-c = (3a? + 2b? - c?, 3a? + 2b? - c?, 3a? + 2b? - c?)
Substituting in the given values, we get:
3a+2b-c = (3(-1) + 2(0) - (-3), 3(1) + 2(2) - (2), 3(1) + 2(-2) - (0))
= (0, 9, -2)
b) The coordinates of vector -a+2c-d are (-5,3,-6).
We can calculate this by using the following formula:
-a+2c-d = (-a? + 2c? - d?, -a? + 2c? - d?, -a? + 2c? - d?)
Substituting in the given values, we get:
-a+2c-d = (-(-1) + 2(-3) - (-2), -(1) + 2(2) - (1), -(1) + 2(0) - (-2))
= (-5, 3, -6)