Let v_1, V_2,...,v_k be nonzero vectors in R^n; We say that the set {v_1, v_2, i
ID: 1721216 • Letter: L
Question
Let v_1, V_2,...,v_k be nonzero vectors in R^n; We say that the set {v_1, v_2, is orthogonal if the following condition holds v_1,v_2 = 0 for EVERY i.j. Recall The dot product (or inner product) of two rectors v_1 = (a_1, a_2, and v_2 = (b_1, B_2, ...,b_n) is defined by v_1.v_2 = (a_1, a_2,...,a_n). (b_1, b_2,...,b_n) = a_1b_1 + a_2b_2 + ... + a_nb_n Determine if the following vectors set of rectors are orthogonal and justifyanswer: 1. v_1 = (1 1 1), v_2 = (-2 1 1),v_3 = (0 1 1) 2. v_1 = (1 0 0), v_2 = (1 1 0), v_3 = (1 1 1)Explanation / Answer
1. Givne three vectors v1, v2 , v3
To check whether this set of vectors is orthogonal or not. check the orthogonality between v1, v2 and v2,v3 and v1,v3
a) V1.V2 = (1)(-2)+(1)(1)+(1)(1) = 0; v1 and v2 are orthogonal
b)v1.v3 = (1)(0)+(1)(1)+(1)(1) = 2 v1 and v3 are not orthogonal
c) v2. v3 = (-2)(0)+(1)(1)+(1)(1) = 2 v2 and v3 are not orthogonal
Therefore the given set of vectors is not orthogonal
2.
a) v1.v2 = (1)(1)+(0)(1)+(0)(0) = 1 v1 and v2 are not orthogonal
this itself is sufficient to show that the given set is not orthogonal
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