Show that the vectors a = 3i-j+4k, b = i-3j-2k and c = 4i-3j+2k are linearly...

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Show that the vectors a = 3i-j+4k, b = i-3j-2k and c = 4i-3j+2k are linearly independent. Find numbers a, 3 and y such that d = 2i + 3j – k can be expressed in the form d = aa + 3b +7c. - Prove that (i) the three points A(1, 4, 2), B(3,2, 4) and C(5,0,6) are collinear, (ii) the four points P(2, –1, 1), Q(1,3, -2). R(-2, 1, -3) and S(3,2,0) are coplanar. . If a = i+ 3j – k, b = 2i + 4j – 2k and c = -i+ 2j + 4k, find a mumber A such that d = a +b + Ac is parallel to the yz-plane. Show that the vectors a = 3i-j+4k, b = i-3j-2k and c = 4i-3j+2k are linearly independent. Find numbers a, 3 and y such that d = 2i + 3j – k can be expressed in the form d = aa + 3b +7c. - Prove that (i) the three points A(1, 4, 2), B(3,2, 4) and C(5,0,6) are collinear, (ii) the four points P(2, –1, 1), Q(1,3, -2). R(-2, 1, -3) and S(3,2,0) are coplanar. . If a = i+ 3j – k, b = 2i + 4j – 2k and c = -i+ 2j + 4k, find a mumber A such that d = a +b + Ac is parallel to the yz-plane.