The dot product is the sum of the product of the first components in each vector and the product of the second components: [a₁, a₂]·[b₁, b₂] = a₁b₁ + a₂b₂.

[2, 1, -4] x [-1, -2, 1] = [-7, 2, -3] = -7i + 2j -3k

Alternatively, you can directly compute crossP([2, 1, -4], [-1, -2, 1]) without storing the vectors to a and b.

The vector [-7, 2, -3] is perpendicular to both [2, 1, -4] and [-1, -2, 1].

The particle follows an elliptical path.

The velocity vector points in a direction that is parallel to the tangent to the curve at the point when
t = /4: The point on the curve in this case is .

For the motion, the acceleration vector points opposite the direction of position vector.

The projectile reaches its highest point about 1.9 seconds after it was fired and it is slightly more than 59 feet above the ground, as shown by the y coordinate.

The projectile reaches its highest point about t = 1.924 seconds after it was fired.

The maximum height of the projectile is about 59.22 ft.

[-15,15] x [-15,15]

Solved Graphically	Solved Analytically

The maximum height occurs about 3.7 or 3.8 seconds after the projectile was launched.