यदि `A=A_(x)hati +A_(y)hatj +A_(z) hatk, B=B_(x)hati +B_(y)hatj +B_(z)hatk`
तथा `R= A+ B = R_(x)hati + R_(y)hatj+ R_(z)hatk` हो, तो `R_(x)` होगा

Options

A. `A_(x)+A_(y)`
B. `A_(x)+B_(x)`
C. `A_(x)+A_(z)`
D. `A_(y)+B_(x)`

Answer

B

Explanation

`:.R=A+B`
`rArr R=(A_(x)hati+A_(y)hatj)+(B_(x)hati+B_(y)hatj)`
`R=(A_(x)+B_(x))hati+(A_(y)+B_(y)) hatj`
`=A_(z)hatk +B_(z)hatk =(A_(z)+B_(z))hatk…(i)`
प्रश्नानुसार,
`R=R_(x)hati +R_(y)hatj+R_(z)hatk…(ii)`
समी (i) व (ii) की तुलना करने पर,
`R_(x)=A_(x)+B_(x), R_(y)=A_(y)+B_(y)`
और `R_(z)=A_(z)+B_(z)`