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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: M-D on April 14, 2013, 07:28:56 am

Title: vector and scalar projections
Post by: M-D on April 14, 2013, 07:28:56 am

hi,

i have the vector u=(2,1,-1,5) and v=(1,1,-2,-1). the dot product between them is zero which means that they are perpendicular to each other. I need to find the scalar projection of v on to u and the scalar projection of u on to v. is it still possible to find these scalar projections when the vectors are perpendicular to each other?

thanks in advance

Title: Re: vector and scalar projections
Post by: nubs on April 14, 2013, 08:44:45 am

It will just be zero

Title: Re: vector and scalar projections
Post by: lzxnl on April 14, 2013, 10:08:22 am

As nubs said, the answer is zero.
If you use the vector resolute formula, which in this case is u.v/v.v * v, you'll find that the vector resolute is the zero vector. Therefore, the scalar resolute is zero.
OR: Draw out a diagram and you'll see that if you decompose u into two components, one parallel to v and one perpendicular to v, u itself IS perpendicular to v, meaning that there is no parallel component.