Consider the following vectors in R³: Give examples of vectors V1 Enter the vector w in the form [C₁, C2, C3]: 4 = [3] 13 5 B W2 and z = W3 satisfying the following conditions: • All entries of W and Z are non-zero integers. • The vector w is not equal to V₁, V₂,V3 and w E Span(V₁, V₂,V3). • z & Span(V₁, V2,V3). Enter the vector Z in the form [C₁, C2, C3]: W = V3 = Z₁ Z2 Z3 [ 12 3 18

Q1. Consider the following vectors: ---C-(C)-C) 1 2 3 (a) Do the vectors u, v, w span R³7 (b) Is vector p in span{u, v, w}? If it is, find the coefficients #1, #2, #3 of a linear combination p= x₁ + x₂ + x3W

Let the vectors x = (-0.3, –4.6, –3) and y = (4.1, –-2.2, r) Determine the value of r such that the two vectors are orthogonal. Your answer should be the value of r as a decimal number with three digits to the right of the decimal point.

Show that if A⋅(B×C)=0, the three vectors must lie in the same plane.