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With respect to a rectangular Cartesian ...

With respect to a rectangular Cartesian coordinate system, three vectors are expressed as
`vec(a)= 4hat(i)-hat(j), vec(b)= -3hat(i)+2hat(j) and vec(c )= -hat(k)`
Where, `hat(i), hat(j), hat(k)` are unit Vector, along the X, Y and Z-axis respectively. The unit vectors `hat(r )` along the direction of sum of these vector is

A

`hat(r) = (1)/(sqrt3) (hat(i) + hat(j)- hat(k))`

B

`hat(r) = (1)/(sqrt2) (hat(i) + hat(j) - hat(k))`

C

`hat(r) = (1)/(3) (hat(i)- hat(j)- hat(k))`

D

`hat(r)= (1)/(sqrt2) (hat(i) + hat(j) + hat(k))`

Text Solution

Verified by Experts

The correct Answer is:
A
`vec(r)= vec(a) + vec(b) + vec(c) = 4 hat(i)- hat(j)- 3hat(i) + 2hat(j)- hat(k)= hat(i) + hat(j) - hat(k)`
Unit vector `hat(r)= (vec(r))/(|r|)= (hat(i) + hat(j) - hat(k))/(sqrt(1^(2) + 1^(2) + (-1)^(2)))= (hat(i) + hat(j) - hat(k))/(sqrt3)`
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