Title: How do I find a vector that is orthogonal to two other vectors? Post by: riza on Jan 27, 2013 Let a = (-4, -8, -4) and b = (-3, -2, 0) be vectors. Find the scalar, vector, and orthogonal projections of b onto a. How do I find the orthogonal component?
Also: Webwork 3 problem 2: Find a vector orthogonal to both <3, 5, 0> to <0, 5, -2> of the form <1, _, _> I don't know what finding the normal vector of the normal vector means. Title: How do I find a vector that is orthogonal to two other vectors? Post by: rizwan440 on Jan 27, 2013 A vector orthogonal to two other vectors will be the cross product between the two vectors.
cross product is defined as: |--i--j--k--| |a1a2 a3| = |b1b2 b3| this will be (a2b3-a3b2)i + (a3b1-a1b3)j + (a1b2-b1a2)k = -10i + 6j + 15k = <-10, 6, 15> multiplying a vector by a constant doesn't change its direction, therefore (-1/10)<-10, 6, 15> is still orthogonal to both. this vector is <1, -.6, -1.5> For the first part, the scalar component of b onto a is given by: (a (dotproduct) b)/|a| the vector component is the scalar component times a/|a|, the unit vector in the direction of a the orthogonal component isn't something ive heard referred to like that, but my guess is that it is the vector distance orthogonal to a up to b.. you could find this by doing the scalar component minus b or by taking a(dotprod)b=|a||b|cos(theta), solving for theta. orthogonal component would be bsin(theta). |