Let 0 = - be the measure of the angle between the vectors u and 0.If ||T'|| = 6 and ||D'|| = 4, then compute CA) || 3 7- 2 u|| (B) ||u + 3 7'|| (C) ū • (T + 2 v) (D) (U + 3 v') •(2 u-7)

Q: 6. What is the measure of the angle 0 between the vectors u : = (6, 2, 1) and 7 = (−4, 1, 2)?

A:

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Q: Find a vector parallel to the line of intersection of the planes 2x + 3y – z =11 and 4x + 2y – 3z =…

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A:

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Q: Let f(x, y) = 5y² In(4x). Then Duf(1,4) in the direction of the vector (-2,-2) is

A: The explanation of answer as follows

Q: find a vector parametrization for the line with thegiven description. Passes through (1, 1, 1) and…

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 6 - -x + 3y + z = 7 Find the normal vector,…

A:

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Q: Find volume V(S) of the parallelepiped S in R3 determined by the (3,4,1); v3 following vectors: vị =…

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A: Let's find.

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A:

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Q: (B) Show that the area of triangle is - ÁxB (Using Vector method)

A: Let, a parallelogram be:

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Q: For which positive value of x are the vectors (-14x, 2, 1), (2, 3.x², –10) orthogonal?

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Q: Let a be the angle between the vectors u=(-3,4,0) and v=(-4,3,0). Then

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Q: Let f(x, y) = 5y² ln(4x). Then Duf(1,4) in the direction of the vector (-2, –2) is

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Q: Find a unit vector u in the direction of v = 〈6, -1〉. Verify that ⎥⎥ U⎥⎥ = 1

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Q: -2 - are the vectors U, = %3D Ug = %3D in M22 are lineor ly depon dent linearly in dependet.

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.