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vector revision

• its direction is perpendicular to the

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

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