1 / 9

Vectors in Space 11.2

Vectors in Space 11.2. JMerrill , 2010. Rules. The same rules apply in 3-D space: The component form is found by subtracting the coordinates of the initial point from the corresponding coordinates of the terminal point. Two vectors are = iff their corresponding components are =.

min
Download Presentation

Vectors in Space 11.2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Vectors in Space11.2 JMerrill, 2010

  2. Rules • The same rules apply in 3-D space: • The component form is found by subtracting the coordinates of the initial point from the corresponding coordinates of the terminal point. • Two vectors are = iff their corresponding components are =. • The magnitude (length) of v • Vector addition still means you add the value in the xplace, the y place, and the z place

  3. Rules • Scalar multiplication still means you distribute the scalar over the component form • The dot product of • If the dot product = 0, then the vectors are orthogonal. • The angle between two nonzero vectors u and v is

  4. Finding the Component Form of a Vector • Find the component form and magnitude of vector v having an initial point of (3,4,2) and a terminal point of (3,6,4) • The component form is • The magnitude is

  5. Finding the Dot Product of Two Vectors • Find the dot product of and • Remember the dot product is a scalar, not a vector.

  6. Find the Angle Between Two Vectors • Find the angle between u = and v =

  7. Parallel Vectors • Vector w has an initial point (1,-2,0) and a terminal point (3,2,1). Which of the following vectors is parallel to w? • A. u = <4,8,2> B. v = <4,8,4> • Put w into component form <2,4,1> • Vector u is the answer because it is just double vector w. U can be written as 2<2,4,1>

  8. Using Vectors to Determine Collinear Points • Determine whether the points P(2,-1,4), Q(5,4,6), and R(-4,-11,0) are collinear. • The points P,Q, and R are collinear iff the vectors PQ and PR are parallel. • Because PR = -2PQ, the vectors are parallel. • Therefore, the points are collinear.

  9. Finding the Terminal Point of a Vector • The initial point of v = <4,2,-1> is P(3,-1,6). What is the terminal point? • We use the initial point of P(3,-1,6) and the terminal point of Q(q1, q2, q3) • PQ = <q1–3, q2 -(-1), q3–6> = <4,2,-1> • The 1st term = the 1st term, the 2nd term = the 2nd term… So, q1–3 = 4, q2 -(-1) = 2, q3–6 = -1 • Point Q = (7, 1, 5)

More Related