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Q.

With respect to a rectangular cartesian coordinate system, three vectors are expressed asa→ = 4i^−j^, b→ = −3i^+2j^ and c→ =−k^where i^,   j^,  k^ are unit vectors, along the X, Y and Z-axis respectively. The unit vector along the direction of sum of these vector 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

r→ = a→+b→ +c→ = 4i^−j^−3i^+2j^−k^   =  i^+j^−k^r^ = r→|r| = i^+j^−k^12+12+(−1)2 = i^+j^−k^3
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