Write a vector equation, parametric equations, and symmetric equations for a line.

Q: rotate the vector 90 degrees counter clockwise about the origin.  ,

A: Let's rotate vector 90 degrees counter clockwise about origin.

Q: In Cartesian coordinates, the position vector at point (3, 40, 1) is represented by

A:

Q: Write unit vector for AB in component form when point A = ( 0,0 ) and point B = (-4, 8 ). %3D %3D

A: Formula: for the vector a→ the unit vector a^ is a^=a→|a→|

Q: 3) |m| = 68, 45°

A:

Q: Give the equation of the line in vector form, parametric form and symmetric form. The line through…

A:

Q: If the wind is blowing from the east at 47 km/h and an airplane is on a heading of 155° with an…

A:

Q: Find the component form and the magnitude of the vector v. Initial Point Terminal Point (-2, 7) (19,…

A:

Q: Vector D represents: B A +B A -B C +B A +C

A: I am attaching image so that you understand each and every step.

Q: 8) An airplane is on a heading of 065° at 350 km/h and an 75 km/h wind is blowing from 310⁰.…

A: 0

Q: Find the magnitude of the vector (-6, 3). Write your answer in simplified radical form.

A:

Q: Write the vector v = ⟨2, -4, 4⟩ as a product of its magnitude and a unit vector with the same…

A: Given vector is  v=2,-4,4 Magnitude of vector v  is v=(2)2+(-4)2+(4)2=4+16+16=36=6 Now, unit vector…

Q: Explain how to write a vector in terms of its magnitude and direction.

A: A vector is a geometric representation of magnitude and direction with respect to the set of…

Q: Rotate the vector (5,1) 90° clockwise about the origin. ([ ? ],[ ])

A: We need to rotate the following vector 90° clockwise about the origin x,y = 5,1

Q: Find the direction of the vector, in degrees, of the vector 21 - 21. No need to indicate the un

A: Recall; Let ai+bj be the vector, Direction of the vector is θ=tan-1ba We have, a=2, b=-2

Q: How can we find the cartesian equation from a vector equation?

A: Equation of line in vector form is:r→=a→+λb→Where,a→=x1i→+y1j→+z1k→ b→=b1i→+b2j→+b3k→

Q: f A = (1, -3, 2) and B = (3, 4, -5), what is B - A? Draw the vector diagram. %3D

A: Topic:- vector

Q: Given vector (-2,6) and a point (3,2) a. Write a vector equation  b. Write the vector equation as…

A:

Q: What is the vector shown in component form? Enter your answer by filing in the boxes.

A: Consider the vector

Q: An airplane is flying with a constant altitude at a speed of 475 mph in a direction 25° north of…

A:

Q: How long is the shadow cast by a 540-foot tower when the sun's rays follow the vector [6,10,-27]?…

A:

Q: 15. An airplane is flying at an air speed of 420 km/h on a heading of 210°. A 45-km/h wind is…

A:

Q: A line has y-intercept 11 and z-intercept -13. Find a vector equation of the line.

A: The line has y-intercept 11 and z-intercept -13. So the line passes through points A(0,11,0) and…

Q: In which direction does the altitude increase most rapidly at the point (300, 300)? Your answer…

A: Part (d): The altitude remains constant along each curve. It rapidly decreases along the direction…

Q: Draw the vector V that goes from the origin to the given point. Then write V in componentform (a, b)…

A: The given vector is -2,5.

Q: Write a vector equation and a scalar equation for a plane.

A:

Q: What is the component form of a vector with a magnitude of 17 and a direction of 125°?

A: We have to find the component  form of the vector with given magnitude  and direction.

Q: A vector is a ray that tells what direction True or false?

A: Given: A vector is a ray that tells direction. To determine: Whether the given statement is true or…

Q: find a vector equation and parametric equations and symmetric equation containing (a,b,c) parallel…

A: To find the vector equation, parametric equation and symmetric equation containing the point (a,b,c)…

Q: an example of a (nonzero) vector perpendicular to ?⃗ = ⟨−17, 3, −6⟩. Please give full explanation…

A:

Q: Write the vector (-7,- 5) as a linear combination of the unit vectors i and j. (-7,-5) =- 7i - 5j…

A:

Q: Find the component form of the indicated vector.

A: The given question belonging to the vector in which we have to find the value of subtraction of the…

Q: Draw vectors representing the course of a ship that travels      75 miles on a course with heading…

A: It is known that the heading of an object is the angle measured clockwise from due north to the…

Q: Consider the point P(-2,3) on the coordinate system. Describe geometrically the position vector…

A: Given point P (2,3)

Q: Wete a system of equations that is equivalent to the vector equation: 国-

A: The solution to the given question is explained below.

Q: Write the vector shown above in component form. Vector Note: In the graph, each box is 1 unit by 1…

A: In the given problem we have to find the component form of given vector . We find component by find…

Q: write the equation of the line passing through P with direction vector d in (a) vector form and (b)…

A: Given the point P=(-4,4) and the direction vector d=11We need to find the equation of line passing…

Q: Write the vector shown above in component form. Vector ww Note: In the graph, each box is 1 unit by…

A:

Q: Problem: If the wind is blowing from the east at 47 km/h and an airplane is on a heading of 155°…

A: Draw the vector diagram, which is given below

Q: Find a vector equation and parametric equation

A: Given, the point (2, 2.6, 3.1) and parallel to the vector 2i + 3j - k.

Q: The four points A, B, C, D have position vectors pi, j+qk, k and i+j respectively, where p and q are…

A: In this question, we find the lines in vector form and check the angle between two line are…

Q: ZA B side of cube = 10 cm 1. write vector notation in Cartesian coordinates 2. what is the length of…

A:

Q: Find the component form and the magnitude of the vector v. Initial Point Terminal Point (-4, 6) (17,…

A:

Q: Draw the vector V that goes from the origin to the given point. Then write V in componentform (a, b)…

A: Let the initial point Pp1,p2 and the terminal point Qq1,q2.The component form of a vector…

Q: A vector with magnitude 4 points in a direction 115 degi Write the vector in component form. Vector…

A: given magnitude = |v| = 4angle ∅=115°

Q: Write the polar form of the vector 3 + 4i.

A: This is a problem of complex analysis.

Q: Sketch the vector ? = ⟨−2, 4⟩.

A: Given: Consider vector V=<-2, 4>

Q: Find the unit vector in the direction of (3, -2). Write your answer in component form. Do not…

A: We will find the unit vector.

Q: 3. Determine the vector equation for the line with symmetric equations X-3.922.231.

A: Compare the given equation with x-x1a=y-y1b=z-z1c so, we get the values x1=3y1=-2z1=1a=4b=5c=3

Q: In vector form (as in Exercises 5 and 6), find an equation for the line through the point (4, – 3,…

A: Given: The line passing through the point 4,-3,7 and with direction vector 4,2,-3. Concept used: The…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.