1. A vector in three dimensions can be written in either of two forms: in coordinate form as v = (a,, az, az) and in terms of the vectors i, j, and k as v = The magnitude of the vector v is | v | = So (4, -2, 4) = i+ j+ k and 7j - 24 k =

Q: a= b=

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Q: Find two vectors v1 and v2 whose sum is (-5, –5, 5), where vi is parallel to a =(0, –1, –2) while v2…

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Q: Find the sum of the vectors (–1,4) and (6, –2) and illustrate geometrically.

A: A vector V→=a,b can be represented on the cartesian plane, From the vector law of addition,…

Q: Find vectors u and v whose initial and terminal points are given. Determine whether u and v are…

A: The u vector can be computed as: u=6-1i+11-1ju=5i+10j

Q: Find a vector, w, which is perpendicular to the vectors where u = 101-20 +14k and v=-20 +10ĵ-5k W +…

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Q: Given vector v = (-6, 4), find -0.5v graphically by stretching the vector by its tip and then…

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Q: Given vectors a = (-4,3) and b = (2,9), what are the components of vector -a – b? (а) (-6, —6)…

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Q: Let A = (-3, 4), B = (-2, b), C = (1, 6), and D = (a, 2). Then AB and DC are opposite sides of the…

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Q: A vector has components A₁, A₂ and 43 in a right-handed rectangu The coordinate system is rotated…

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Q: Sketch 2v, -w, v+w, and 2v-w for the vectors in Figure 24. 5 y 4 3 v = (2,3) 2 1 w = (4, 1)

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Q: 6. Write DÉ as a linear combination of the vectors i and j a) D (9,-6) E (-7, 2) first write in…

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Q: a. Write the vector (23,-12, -19) as a linear combination of a₁ = (3, -2, -1), a2 (2, -3, -1) and ã3…

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Q: Suppose we know that Write A 6 as a linear combination of the vectors 5 8- 5 6 = 0 H + 6 1 1 -DE-B H…

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Q: If the vectors ü =[-9, a, 15] and V= [b, 2, - 5] are collinear, then: a = 6 and b = -3 Oa = -6 and…

A: by using collinear concept

Q: A vector in three dimensions can be written in either of two forms: in coordinate form as v = (a₁,…

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Q: 5. Name each vector then write the vector in component form

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Q: If a, b and c are three non-coplanar vectors, then find the value of a.(bxc) b.(cxa) c.(bxa) +…

A: Use the properties of vector box product as follows: a→.(b→×c→)=[a→ b→ c→]=[b→ c→ a→]=[c→ a→…