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Question:

Write a unit vector in the direction of the sum of the vectors →a = 2→i + 2→j - →k and →b = 2→i + →j - →k

Solution:

Here, →a = 2→i + 2→j - →k and →b = 2→i + →j - →k
→a + →b = (2→i + 2→j - →k) + (2→i + →j - →k) = 4→i + 3→j - 2→k
|→a + →b| = √4² + 3² + (-2)² = √16 + 9 + 4 = √29
Therefore, required unit vector = (→a + →b) / |→a + →b| = (4→i + 3→j - 2→k) / √29