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

Q: Find a vector b such that |b| = 1/2 that is parallel to a = but with opposite direction.

A: Given that: |b|=12a=<-6, 3, -2>

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

A:

Q: Q12: Let vector v = (1, 3) and vector w=(-4,-2). Write vector v as the sum of two orthogonal…

A:

Q: Let L be the line y = 6 – 4x in R?. Find vectors a and b so that v = a+tb is a vector equation for…

A: Vector equation of line

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…

A:

Q: Let P(-1, 1, 3) and Q(-3, 1, 5) be points in R3. Find the components, magnitude and direction angles…

A:

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

A:

Q: Complete the two-column proof. Given: HO PE, HE » PO Prove: 20 a ZE 1) HO PE 1) 2) HE PO 2) 3) 3)…

A: Given HO≅PEHE≅PO To prove ∠O≅∠E

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

A:

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

A:

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

A:

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 = → ->…

A:

Q: Describe the Z-axis in R as the span of a vector. Can you describe it as the span of other vectors…

A:

Q: What vector v is given by the coordinate vector B = { 9x +4, 4x + 6 }. [3] ? B

A:

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

A:

Q: (b) 4x Find any values of x such that the vectors 3 and are parallel X-1 to each other.

A:

Q: Given the points A: (-5,4,0) and B: (2,-2,4), find the vector u = AB ú=< -3 X 2 X 4

A:

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

A:

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

A:

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.

Q: Let u = (2, 0), v = (-2, -4), and w = (-4, 1). Find the vector æ that satisfies 4u – v+ x = 9x + w.…

A: Solution:-

Q: For any vector v = (a, b, 0), where a and b are any nonzero real numbers, Select one: True False vok…

A: Here I have written the notion, I have used in my solution

Q: Let ū = (3,2), v = (-2, –2), and w = (-4,3). Find the vector x that satisfies 5u – v +x = 7x + w. |…

A: Given that u→=3,2v→=-2,-2w⇀=-4,3

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.