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When is a cross product zero?
When the component vectors have equal or opposite directions (sin(Θ) = 0) i.e. the vectors are parallel.
1 1 Check whether the following set of vectors is LD or LI?
(i) They are linearly dependent since the 2nd vector is twice the 1st vector. All 3 vectors lie in the x-z plane, so they don't span 3D space. (ii) They are linearly independent. Note that the cross-product of the first two is (-1,1,1). If the third vector is not perpendicular to the above cross-product, then the third vector does not lie in the plane defined by the first two vectors. (-1,1,1) "dot" (1,1,-1) = -1+1-1 = -1, not zero, so 3rd vector is not perpendicular to the cross product of the other two.
What are the products of the terms on the diagonals when two ratios are compared?
The products of the diagonal terms of two ratios is known as the cross product. This term is more often used in reference to vectors, however.
When are vectors said to be perpendicular?
Perpendicular means that the angle between the two vectors is 90 degrees - a right angle. If you have the vectors as components, just take the dot product - if the dot product is zero, that means either that the vectors are perpendicular, or that one of the vectors has a magnitude of zero.
How do you take dot product of two vectors?
Multiply the product of their magnitudes by the cosine of the angle between them.
