Vectors and the Geometry of Space

Question

Find a unit vector in the same direction as a=(8,10,4).

Answer 1

Solution:

Vector a can be written as a^→ = 8i+10j+4k , and unit vector of a is u_a = a^→ / | a|

where the magnitude |a| = √( 8²+10²+4²) = √180 = √(36x5)= √36 . √5 = 6√5

u_a = 8i + 10j + 4k / 6√5 = (8/6√5)i + ( 10/6√5)j + ( 4/6√5)k = ( 4/3√5) i + (5/3/√5) j + (2/3√5) k rationalize to get rid of the √ from the denominator multiply by √5 / √5 for all terms and simplify you get:

u_a = (4√5/15) i + (√5 / 3) j + ( 2√5/15) k