2/7i^+aj^+6/7k^ is a unit vector when a is ______________ ?

1 Answer
Apr 17, 2018

#a = +-3/7#

Explanation:

Magnitude of a unit vector is #1#

So, magnitude of vector #2/7hati + ahatj + 6/7hatk# should be #1#

#sqrt((2/7)^2 + a^2 + (6/7)^2) = 1#

Squaring on both the sides

#4/49 + a^2 + 36/49 = 1#

#a^2 + (4 + 36)/49 = 1#

#a^2 + 40/49 = 1#

#a^2 = 1 - 40/49#

#a^2 = (49 - 40)/49#

#a^2 = 9/49#

Square root on both the sides

#a = sqrt(9/49)#

#a = +-3/7#