State whether the vectors are parallel, orthogonal, or neither. 5) v = 2i + j, w =i- 2j 6) v = 2i + 4j, w = 4i - 2j 7) v = 2i - j, w= 4i - 2j 8) v = 3i + 4j, w = 6i + 8j 9) v = 4i - 2j, w = 4i + 2j 10) v = i+ 3j, w =i- 2j

Q: Verify the Pythagorean Theorem for the vectors u and v. u = (1, -1), v = (1, 1) Are u and v…

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A: Now

Q: True or false: Given two nonzero vectors v and w, v can be decomposed into two vectors, one parallel…

A: Given: Two nonzero vectors v and w, v can be decomposed into two vectors, one parallel to w and the…

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Q: find "a" so that the vectors v=i-ja and w=2i+3j are orthaganal?

A: Given,  v=i-ja and w=2i+3j Two vectors are orthogonal if and only if their dot product is zero

Q: Q1. Given three vectors A = -a,+2a,+3a, B = 3a,+4a,+5a, and C = 2a, -2a,+7a,, compute : a) Angle…

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Q: snip

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Q: The unit vector perpendicular to the vectors n1= i-j+3k ,n2=2i+j+3k is a vector?

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Q: Show that if u+ v and u - v are orthogonal, then the two vectors must have the same length. What…

A: Hence the two vector u and v have same length.

Q: ors a = 6i + 7j + 6k and b = 4i − j + 8k, where i, j, and k are mutuallyperpendicular unit vectors…

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Q: . If u and v are nonzero vectors in Rº, why do the equa- tions u · (u x v) = 0 and v · (u x v) = 0…

A: The dot product of orthogonal vectors is equal to zero.

Q: 24. Verify the parallelogram law for vectors u and v in R": |u + v|l° + |[u – v||² = 2||u||² +…

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Q: Show that if the vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

A: Given: The vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

Q: True or false: Given two nonzero vectors v and w, v can be decomposed into two vectors, one parallel…

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Q: 2. Determine the value of a for which the vectors b = ai – 5j+3k and 7 =i +2}-ak are orthogonal ?

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Q: Is it possible to have ||u−v|| = ||u + v|| if u and v are nonzero vectors? Justify your conclusion…

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Q: 19. Show that the pair of vectors 8i+j and i-8j is perpendicular.

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Q: If u, v are vectors such that |u || - 3, ||v|| - V5, and u v- 1, what is |u + v|| ?

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Q: 10. Which of the vectors U =, V = and W = are in the same plane?

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Q: O let A = i+2j-K, B=-i+j+K, Esi+k, 5z i+2j-K which vectors are: @ perpen dicular Parallel

A: Our are objectives to check which vectors are parallel and which vectors are perpendicular

Q: Show that the points whose position vectors 2i+ 3j – 5k , 3i +j – 2k and 6ỉ – 5j + 7k are collinear?

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Q: Find the two unit vectors orthogonal to both a = 3j + 2k and b = -i- 2k. O A -61 - 2j + 3k and 6i+…

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Q: 2. (a) Compute ||(1,2, 3)||- (b) Find the angle between the vectors (1, v3) and (1,0).

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Q: Are the vectors v = 2i + 3j and w = 6i - 4j orthogonal?

A: Are the vectors v = 2i + 3j and w = 6i - 4j orthogonal?

Q: 64. Show that if u + v and u – v are orthogonal, then the vectors u and v must have the same length.…

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Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) (10, -12, -2) %3D V =

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A:

Q: Calculate the triple product u · (v × w) of the vectors u = 3i − 2j − 5k, v = i + 4j − 4k, w = 3j +…

A: Calculate the triple product u · (v × w) of the vectors u = 3i − 2j − 5k, v = i + 4j − 4k, w = 3j +…

Q: 3. Find the angles between the vectors: a. u = 2i + j, b. u = 2i – 2j + k, v = 3i + 4k v = i + 2j –…

A: