Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §11.3 Cross Products and Determinants, #45 · Multivariable Calculus · Vectors & geometry

(1) The projections of … and … onto the … plane are…

(1) The projections of $A = a_{1} i + a_{2} j + a_{3} k$ and $B = b_{1} i + b_{2} j + b_{3} k$ onto the $x y$ plane are ______.
(2) The parallelogram with sides $A$ and $B$ projects to a parallelogram with area ______.
(3) General fact: The projection onto the plane normal to the unit vector $n$ has area $(A \times B) \cdot n$ . Verify for $n = k$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §11.3 Cross Products and Determinants, #45

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