# Question Video: Expressing a Given Vector in Cartesian Coordinates Mathematics • 12th Grade

Given that π = 9π’ + 3π£ + 7π€, write vector π in Cartesian coordinates.

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### Video Transcript

Given that vector π is equal to nine π’ plus three π£ plus seven π€, write vector π in Cartesian coordinates.

Vector π is currently written in terms of the fundamental unit vectors π’ hat, π£ hat, and π€ hat. These can be shown on the three-dimensional coordinate plane as follows. The unit vector π’ hat corresponds to one unit in the π₯-direction. The unit vector π£ hat corresponds to one unit in the positive π¦-direction. Finally, the unit vector π€ hat corresponds to one unit in the positive π§-direction.

We can write any vector given in this form in terms of its Cartesian coordinates. This is written π₯, π¦, π§ as shown. Vector π is equal to nine π’ plus three π£ plus seven π€. Therefore, our π₯-value is nine, the π¦-value is equal to three, and the π§ or π§-value is equal to seven. The vector π nine π’ plus three π£ plus seven π€ written in Cartesian coordinates is nine, three, seven.