Find in exact form the unit vector in the same direction as #veca=4hati-7hatj#?

2 Answers
Mar 22, 2018

#hata= 4sqrt65/65hati-7sqrt65/65hatj#

Explanation:

Given: #veca=4hati-7hatj#

The unit vector is:

#hata=veca/|veca|#

#|veca| = sqrt(4^2+(-7)^2)#

#|veca| = sqrt65#

#1/|veca|=sqrt65/65#

Substituting into the equation for #hata#:

#hata= 4sqrt65/65hati-7sqrt65/65hatj#

Mar 22, 2018

#ulu_a=4/sqrt65hati-7/sqrt65hatj#

Explanation:

#"the unit vector in the same direction as "vec(a)#

#•color(white)(x)u_a=vec(a)/|vec(a)|#

#"where "|vec(a)|=sqrt(x^2+y^2)#

#"here "x=4" and "y=-7#

#rArr|vec(a)|=sqrt(4^2+(-7)^2)=sqrt65#

#rArru_a=4/sqrt65hati-7/sqrt65hatj#