The portal has been deactivated. Please contact your portal admin.

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

Given that 𝐀 = 9𝐒 + 3𝐣 + 7𝐀, write vector 𝐀 in Cartesian coordinates.

01:27

Video Transcript

Given that vector 𝐀 is equal to nine 𝐒 plus three 𝐣 plus seven 𝐀, write vector 𝐀 in Cartesian coordinates.

Vector 𝐀 is currently written in terms of the fundamental unit vectors 𝐒 hat, 𝐣 hat, and 𝐀 hat. These can be shown on the three-dimensional coordinate plane as follows. The unit vector 𝐒 hat corresponds to one unit in the π‘₯-direction. The unit vector 𝐣 hat corresponds to one unit in the positive 𝑦-direction. Finally, the unit vector 𝐀 hat corresponds to one unit in the positive 𝑧-direction.

We can write any vector given in this form in terms of its Cartesian coordinates. This is written π‘₯, 𝑦, 𝑧 as shown. Vector 𝐀 is equal to nine 𝐒 plus three 𝐣 plus seven 𝐀. Therefore, our π‘₯-value is nine, the 𝑦-value is equal to three, and the 𝑧 or 𝑧-value is equal to seven. The vector 𝐀 nine 𝐒 plus three 𝐣 plus seven 𝐀 written in Cartesian coordinates is nine, three, seven.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.