Scalars and Vectors, Now with î and ĵ

You'll learnto build a vector from its signed î and ĵ components before finding its magnitude, angle, and sum.

Six units of î, negative eight of ĵ — the exact arrow the lesson froze on the page, now assembled head-to-tail in front of you. Watch what the signs actually do, why the magnitude is 10 and not −2, and how two vectors add without ever leaving component form.

8 STEPS · 6 QUICK CHECKS · v3

COMPONENT PLANE

Before you start

What you're looking at

A component plane with one dashed arrow from the origin — a drone velocity v = 6î − 8ĵ m/s, its magnitude marked unknown.

The question

For this arrow, what are its components, its speed (the magnitude), and its direction?

Watch for

The signs the components carry, and why the magnitude comes out 10, not 6 + (−8) = −2.

What the symbols mean

î = one unit of +x, ĵ = one unit of +y; the dashed arrow is velocity; the readout tracks components, speed, direction.

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