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Q.

With respect to a rectangular cartesian coordinate system, three vectors are expressed asa = 4i-jb = -3i +2jc = -kwhere i, j, k are unit vectors, along the x, y and z-axis respectively. The unit vector r along the direction of sum of these vectors is

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a

r=13(i+j−k)

b

r=12(i+j−k)

c

r=13(i−j+k)

d

r=12(i+j+k)

answer is A.

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Detailed Solution

Given that,a = 4i-j,b =-3i+2j and c=-kThe sum of three vectors = i + j - kThe unit vector along the direction of sunr=i+j−k1+1+1=13[i+j−k]
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With respect to a rectangular cartesian coordinate system, three vectors are expressed asa = 4i-jb = -3i +2jc = -kwhere i, j, k are unit vectors, along the x, y and z-axis respectively. The unit vector r along the direction of sum of these vectors is