{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

vector revision

• its direction is perpendicular to the

Info iconThis preview shows pages 33–36. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: • Its direction is perpendicular to the parallelogram. θ x a b b bsin θ a ♣ Example 1.26 Question g is vector from A [1,2,3] to B [3,4,5]. ˆ l is the unit vector in dirn from O to A. Find ˆm , a UNIT vector along g × ˆ l Verify that ˆm is is perpendicular to ˆ l . Find ˆn , the third member of a r-h coord set ˆ l , ˆm , ˆn . g l A B [1,2,3] [3,4,5] Answer 1) g = [3 − 1 , 4 − 2 , 5 − 3] = [2 , 2 , 2]. 2) ˆ l = [1 , 2 , 3] / √ 14 3) g × l = vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle ˆ ı ˆ ˆ k 2 2 2 1 2 3 vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle = [2 , − 4 , 2] ⇒ ˆm = [1 , − 2 , 1] / √ 6 4) ˆ l · ˆm = (1 . 1 + 2 . − 2 + 1 . 3) / ( . ) = 0 5) ˆn = ˆ l × ˆm = 1 √ 6 √ 14 vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle ˆ ı ˆ ˆ k 1 2 3 1 − 2 1 vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle Random question 1.27 Q: If ˆ f and ˆg are two unit vectors, what is the magnitude of the vector product ˆ f × ˆg f x g g f θ A: Magnitude is sin θ . Summary 1.28 We’ve revised and discussed ... • Free, sliding and position vectors • Coord frames and Vector components • Equality, magnitude, Addition, Subtraction • Scalar products, Vector Projection, Inner products • Vector Products In Lecture 2 ... • Vector multiple products: • Geometry of Lines and Planes • Solving vector equations • Angular velocity and moments Then the calculus starts...
View Full Document

{[ snackBarMessage ]}

Page33 / 36

• Its direction is perpendicular to the parallelogram θ...

This preview shows document pages 33 - 36. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online