Let v = ( 1, 2 ), Find a vector w with the same direction as v such that || w || = 7.

Q: Let a. h and care vectors such that a = 3. b = 4 and | C| = 5, and (a+b) is perpendicular to -- c.(b…

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Q: Find a vector v such that ||v|| = 20 and v is in the same direction as 15i + 15j

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Q: Let ū = (4, –2), ū = (-2,0), and w = (2, 2). Find the vector x that satisfies Tu – u +x = 5x + w. In…

A: Given Let Plugging the values in the equation:

Q: Assume vectors u = [1, 3,0] and w = [-2, 2, 0]. Find a vector v that is not w but satisfies the…

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Q: Q11: Let vector v = (-7, 5) and vector w=(2, 2). Write vector v as the sum of two orthogonal…

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Q: -> Let a, b and care vectors such that a = 3, | b = 4 and = 5, and (a+b) is perpendicular to c.(b +…

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Q: Find a vector v such that ||v||=20 and v is in the same direction as 15i+15j.

A: The parallel vector of a vector is the scalar multiple of the vector, and if scalar is positive then…

Q: b Find all vectors W (W₁, W2, W3) that satisfy the equation: (3,1,4) x W = (-3,1,2).

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Q: Find the length of the vector x=x= |x|=|x|=

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Q: Find a direction vector for the line containing the origin (0, 0, 0) and the point (2, 3, – 1).

A: The given points are 0,0,0  and  2,3,-1

Q: Express the vector from P(-1, -4, 6) to Q(1, 3, -6) as a position vector in terms of i, j, and k.

A: Given vectors are P-1,-4,6 and Q1,3,-6.

Q: → ->> Let a, b and care vectors such that a = 3₁ | b = 4 and 5, and (a+b) is perpendicular to = → ->…

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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: Let l be a straight line that passes through the origin and is parallel to the vectors…

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Q: The vectors u = (-7, 1, -2) and v = (-28, x, - 8) are parallel if and only if x = - 212 %3D Select…

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Q: Find a vector orthogonal to the line x+y=1

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Q: Let u = (2, −1, −1) and v = (5, -3, 3). A vector with integer components perpendicular to ū and v is…

A: <-6, -11, -1>Explanation:Step 1: Determine how to find the perpendicular vector To find a…

Q: Find a vector in the plane parallel to the line ax + by = c.

A: We know that, Slope of parallel lines are equal Given equation of line is ax + by = c Slope of this…

Q: = ---- -2 8 span of v₁ and v₂? Let V₁ = and y = -5 -3 For what value(s) of h is the vector y in the

A: The given vectors  and .The objective is the find the value of  for which the vector  in the span of…

Q: Let the vector be x = (5,6), determine its coordinates relative to the base B = {(1,1),(-1,2)}}

A: Introduction: When a basis is provided, one can represent a vector belonging to the precise vector…

Q: ? (2,3), (0,0) }

A: Let S=2, 3, 0, 0. We need to find whether the set S spans a line or all of ℝ2.

Q: Find the length of the vector v = (9, 3, 9). ||v|

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Q: -2 Show whether or not the vector bs is a linear combination of the vectors a, = az = and az = that…

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Q: Show that if u and v are vectors in the three-space, then ||u x v||? = ||u|| ||||² – (u · v)²

A: u and v are vectors.

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.