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Let u=⟨8,0,−7⟩.

(a) Find the vector and scalar projections of u onto i.
(b) Find the vector and scalar projections of u onto j.
(c) Find the vector and scalar projections of u onto k

User MKR
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1 Answer

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Final answer:

The question involves finding the vector and scalar projections of the vector u onto the standard basis unit vectors i, j, and k. The results are: for i, vector projection ⟨8,0,0⟩ and scalar projection 8; for j, both vector and scalar projections are 0; for k, vector projection ⟨0,0,-7⟩ and scalar projection -7.

Step-by-step explanation:

The question asks for the vector and scalar projections of the vector u onto the unit vectors i, j, and k. The vector u is given as u = ⟨8,0,−7⟩. The vector projection of u onto any unit vector is the dot product of u with that unit vector times the unit vector itself. The scalar projection is simply the dot product of u with the unit vector.

Vector and Scalar Projections onto i, j, and k

  • i Vector Projection: ⟨8,0,0⟩, Scalar Projection: 8
  • j Vector Projection: ⟨0,0,0⟩, Scalar Projection: 0
  • k Vector Projection: ⟨0,0,−7⟩, Scalar Projection: −7

The vector projections are parallel to the respective unit vectors and the scalar projections are the lengths of these vector projections in the direction of the unit vectors.

User Hardik Lakhani
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