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Find the component of vector A+B along ...

Find the component of vector A+B along
i. X-axis, ii. C.
Given, `A=hat(i)-2hat(j)+3hat(k)andC+hat(i)+hat(j).`

A

`3,(1)/(sqrt(2))`

B

`2,(3)/(sqrt(2))`

C

`5,(2)/(3)`

D

`4.1, (2)/(sqrt(2))`

Text Solution

Verified by Experts

`(a) A+B=(hat(i)-2hat(j))+(2hat(i)+3hat(j))=3hat(i)-2hat(j)+3hat(k)`
i. Component of A+B along X -axis is 3.
ii. Component of A+B=R (say) along C is
`:. R*C=RC cos theta`
`Rcostheta+(R*C)/C=((31hati-2hat(j)+3hat(k))*(hati+hat(j)))/sqrt((1)^(2)+(1)^(2))`
`=(3-2)/(sqrt(2))=(1)/(sqrt(2))`
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