If the vectors a→=iˆ−jˆ+2kˆ,b→=2iˆ+4jˆ+kˆ and c→=λiˆ+jˆ+μkˆ are mutually orthogonal, then (λ,μ)=(2,−3)(−2,3)(3,−2)(−3,2)

If coordinates of A , B and C are ( –1, 0, –3), (2, 3, –1) and (–1, 4, 2) respectively. Find a unit vector perpendicular to both 𝐴𝐵⃗⃗⃗⃗⃗ and 𝐴𝐶⃗⃗⃗⃗⃗ .

A set of three vectors {v1,v2,v3}{𝑣1,𝑣2,𝑣3}   in a vector space is an orthogonal set if each is vector is a non-zero vector, and if every vector is orthogonal with the other two. This means explicitly thatv1⋅v2=v2⋅v3=v3⋅v1=0.𝑣1⋅𝑣2=𝑣2⋅𝑣3=𝑣3⋅𝑣1=0.   So for example ⎧⎩⎨⎪⎪⎛⎝⎜341⎞⎠⎟,⎛⎝⎜5−2−7⎞⎠⎟,⎛⎝⎜1−11⎞⎠⎟⎫⎭⎬⎪⎪{(341),(5−2−7),(1−11)}   is an orthogonal set in R3𝑅3   . Can you find a set of three orthogonal vectors in R3𝑅3   which includes the vector ⎛⎝⎜4−12⎞⎠⎟?(4−12)?     Such a set is

a (non-zero) vector perpendicular to both ⎛⎝⎜−1−50⎞⎠⎟(−1−50) and ⎛⎝⎜−4−13⎞⎠⎟(−4−13) is

Let a=[−3,0,−3]𝑎=[−3,0,−3], b=[0,−1,0]𝑏=[0,−1,0], and c=[0,3,−2]𝑐=[0,3,−2]. Compute (a×b)⋅c(𝑎×𝑏)⋅𝑐.

Find the cross product a × b.a = 8, 0, −3,    b = 0, 8, 0⟨24,0,64⟩ Verify that it is orthogonal to both a and b.