Question

With respect to a rectangular Cartesian coordinate system three vector are expressed as
a=4i-I
b=-3i+2j
c=-k
Where i,j,k are the unit vectors along the x,y and z axis . The unit vector r along the direction of sum of these vectors is ?????

Answer 1

three vectors are ;

a = 4i - j

b = -3i + 2j

c = -k

we have to find unit vector r along the direction of sum of these vectors.

first of all, we should find some of given vectors.

P = a + b + c

= (4i - j) + (-3i + 2j) + (-k)

= i + j - k

so, sum of given vectors is P = i + j - k

now, unit vector along P can be written as P/|P|

so, r^ = P/|P|

where |P| denotes magnitude of P ( i.e., sum of given vectors )

so, |P| = √{1² +(-1)² + 1²} = √3

so, r^ = (i - j + k)/√3

hence, unit vector along the direction of sum of these vector is (i - j + k)/√3

Answer 2

Answer:

Explanation:

a = 4i - j

b = -3i + 2j

c = -k

P = a + b + c

= (4i - j) + (-3i + 2j) + (-k)

= i + j - k

unit vector along P can be written as P/|P|

r^ = P/|P|

where |P| denotes magnitude of P ( i.e., sum of given vectors )

|P| = √{1² +(-1)² + 1²} = √3

r^ = (i - j + k)/√3