If vectors a, b and c are coplanar, show that ↑ ↑- ↑ 11 C -->> a. a a.b a c= 0. ↑ ↑-

Q: ex/IF Ā=i-j+3k and B =2 i+6j+3K Find the vector pricâ+B) and Prj (À-B).

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Q: Let V₁, V2, V3 be linearly independent vectors in R". Show that {v₁ + V₂, V₂ + V3, V3 + ₁} is also…

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Q: The cross product of two vectors u=(2, -3, 1) and v=(0, − 1, 2) is 5. O True O False

A: Here is the solution:

Q: Given three non-zero vectors, a, b & C, is it possible to evaluate a b Explain with an example. •6•²

A: We have given three non-zero vector.

Q: cannot be found in such a general cas explain why. In either case, justify you 2) Let a and b be two…

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Q: (x.yız) (x,9e)x4か t. 22 P( 3-1,0) けこくりん)2

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Q: Let a = (2,3,6) and b = (3,4,2) be vectors.  Compute the cross product aXb

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Q: how that vectors[ A-2i+ 3j - 2k,B=I +2j+ 4k ] are perpendicular to each o

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Q: Show that the vectors 2 -2 2 uj = 2 uz = 3 uz = 7 1 -5 -3 are linearly dependent. Find all r1, x2,…

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Q: Suppose that u and v are vectors in 3-space such that u ||= 5 and u · v= 7. Find: (a) u · u = (b) v…

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Q: find the diJ tance betueen the vectors

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Q: Every vector of R²is linear combination of (-1, 1), (2, –2)? Justify

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Q: 2 A : 10 %3| 0 -1 4

A: To find out solution of homogeneous set of linear equation of A's we have to find the solution of…

Q: Let a and b be two unit vectors. 1) a x (a.b) 2) a . (axb) 3) a . (a+(axb)) 4) (axb) + (bxa)…

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Q: ) The vectors (3,0,0,0), (0,−1,2,1), (6,2,−6,0) and (3,−2,3,3) in ?4 are linearly independent.

A: solve the following

Q: 4. Express PQ-RO+SR-PS+RS as a single vector.

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Q: Let a = (a1, a2), b = (b₁,b2) be vectors in R². The area(a, b) is given by 1b₂-a2b₁. (a.) Show that…

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Q: (c) a-i+25+5k and 6 3i+ 45-E d) ä = 2i + 6j - 4k and 6- -3i - 95 + 6k

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Q: 4 3 2 1 b. -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

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Q: 5 3 -2 -3 w = -3 |; A= 4 -5 2 2 -5 4 -1 . Determine if vector w is in Nul(A)

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Q: 150. Determine the real number a such that vectors a = -3i+2j and b = 2i+aj are orthogonal.

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Q: Express the vector in the form (V= ai+ bj+ck) *, if A(1,0,3) and B is (-1,4,5):

A: Vector from

Q: Show that the vectors X1 = 2e2t and 2et X2 5e3t form a linearly independent set.

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Q: Let V₁, V2, V3 be the vectors in R³ defined by 18 ---A V2 = -14 (a) Is (V1, V₂, V3} linearly…

A: We now solve this questions