With respect to a rectangular cartesian coordinate system, three vectors are expressed as : a = 4 i ^ − j ^ , b = − 3 i ^ + 2 j ^ and c = − k ^ where i ^ , j ^ , k ^ are unit vectors, along the

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With respect to a rectangular cartesian coordinate system, three vectors are expressed as : a = 4 i ^ − j ^ ​ , b = − 3 i ^ + 2 j ^ ​ and c = − k ^ where 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 vector is -

TestHub · Accepted Answer

​ r = a + b + c = 4 i ^ − j ^ ​ − 3 i ^ + 2 j ^ ​ − k ^ = i ^ + j ^ ​ − k ^ r ^ = ∣ r ∣ r ​ = 1 2 + 1 2 + ( − 1 ) 2 ​ i ^ + j ^ ​ − k ^ ​ = 3 ​ i ^ + j ^ ​ − k ^ ​ ​

Mathematics - Vector Question with Solution | TestHub

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