Theory question 108
VectorsGiven that w = 8i + 3j, x = 6i − 5j, y = 2i + 3j and |z| = 41, find z in the direction of w + x − 2y.
Show the model answer
Model answer
w + x − 2y = (8 + 6 − 4)i + (3 − 5 − 6)j = 10i − 8j; its length is √164 = 2√41.
Unit vector = (5i − 4j)/√41.
z = 41 × (5i − 4j)/√41 = √41(5i − 4j) = 5√41 i − 4√41 j.
(If |z| = √41 is meant, z = 5i − 4j.)
Explanation
A vector of given length in a given direction = length × unit vector.