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A particle moves 21m along the vector 6h...

A particle moves `21m` along the vector `6hat(i)+2hat(j)+3hat(k)` , then `14 m` along the vector `3hat(i)-2hat(j)+6hat(k)`. Its total displacement (in meters) is

A

`15hat(i)+2hat(j)+12hat(k)`

B

`9hat(i)+12hat(k)`

C

`9hat(i)+6hat(j)`

D

`24hat(i)+2hat(j)+21hat(k)`

Text Solution

Verified by Experts

The correct Answer is:
D
Total displacement
`=21((6hat(i)+2hat(j)+3hat(k))/(7))+14((3hat(i)-2hat(j)+6hat(k))/(7))`
`=18hat(i)+6hat(j)+9hat(k)+6hat(i)-4hat(j)+12hat(k)`
`=(24hat(i)+2hat(j)+21hat(k))m`
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