What is a unit vector in the direction of the resultant of vectors A = 2i-3j+k , B = i+j+2k and C = 3i-2j+4k?
To find the resultant of vectors A, B, and C, we need to add them together:
Resultant = A + B + C
= (2i - 3j + k) + (i + j + 2k) + (3i - 2j + 4k)
= (2i + i + 3i) + (-3j + j - 2j) + (k + 2k + 4k)
= 6i - 4j + 7k
The unit vector in the direction of the resultant vector is found by dividing the resultant vector by its magnitude:
Magnitude of Resultant = √((6)^2 + (-4)^2 + (7)^2) = √(36 + 16 + 49) = √101
Unit Vector = (6i - 4j + 7k) / √101
Therefore, the unit vector in the direction of the resultant of vectors A, B, and C is:
(6i - 4j + 7k) / √101