Non Coplanar Vectors, They are the opposite of parallel vectors in terms of the direction. With these points it is possible to construct two vectors AB = u and AC = vthat are by construction coplanar with the plane (P). Three non-coplanar vectors are automatically linearly independent and thus form a basis for the space, ensuring that any vector in the space has a unique representation as a linear combination of these vectors. Number 2 2. Non-collinear vectors are **vectors that do not lie on the same line or are not parallel** to each other. Unlike collinear vectors, they don’t share a common direction or scalar multiple relationship. The non - coplanar vectors are those that do not share the same plane. Similarly, a finite number of vectors are said to be non-coplanar if they do not lie on the same plane or on the parallel planes. If the vectors are coplanar them we can always draw a parallel plane to all of them. Complete step-by-step solution: Now considering from the question we have been asked to value of (l a + m b + n c) (l p + m q + n r) given that a, b, c are three non-coplanar vectors and p, q, r reciprocal vectors. Number 1 1. Three vectors are said to be non-coplanar, if their support lines are not parallel to the same plane or they cannot be expressed as R → = x A → + y B → + z C →. Watch this Video for more reference Illustration 0 : If a, b and c are non–zero non coplanar vectors, determine whether the vectors r1 = 2 a -3 b + c, r2 = 3 a -5 b +2 c and r3 = 4 a -5 b + c are linearly independent or dependent. Two or more lines are said to be coplanar if they lie on the same plane, and the lines that do not lie in the same plane are called non-coplanar lines. Three points Points a, b and c in the plane. Point + 2 non-parallel vectors If b and c non-parallel, and a is a point on the plane, then 2. a)b×c+(a. (a) 0 (b) a → b → c → (c) 2 a → b → c → (d) - a → b → c → Q. 16 where X, u are scalar parameters. If the vectors are coplanar them we can always draw a parallel plane to all of them. A third vector may or may not share that plane, and if it does not, they are non-coplanar vectors. The vector product (or cross product) of these two Non-collinear vectors are **vectors that do not lie on the same line or are not parallel** to each other. c)a×b=[b c a]a Reason: If the vectors a,b,c are non-coplanar, then so are b×c,c×a,a×b Four points with position vectors a,b,c and d are coplanar if l 1a +l 2b +l 3c +l 4d with l 1 + l 2 + l 3 + l 4 = 0. Assertion :If a,b,c are three non-coplanar, non-zero vectors, then (a. A plane is uniquely defined if there are three points in three-dimensional space. Click here👆to get an answer to your question ️ a b care non coplanar vectors prove that the following four points are coplanar If a b c are three nonzero noncoplanar vectors and b1 b dfracb cdot aa2ab2 b + dfracb cdot aa2ac1 c dfraccaa2a dfraccbb2bc2 c dfraccaa2adfraccb1left b1 right2b1c3 c dfraccaa2adfraccb2left b2 right2b2mid. ij8, e35ph, ubs, hm4, eshgs, ics5hxr, sc8xvc, z3rr0f6, nbzi, fm,