2-D Vectors
Two-dimensional vectors are fundamental mathematical entities extensively utilized across various fields, including physics, computer graphics, and engineering. Represented by ordered pairs of real numbers, these vectors possess both magnitude and direction, making them pivotal in describing spatial relationships and quantities in two-dimensional space. They play a crucial role in operations such as addition, subtraction, scalar multiplication, and dot product computations. Understanding 2-D vectors is essential for grasping concepts like displacement, velocity, force, and momentum in a plane, offering a foundational framework for problem-solving and analysis in diverse disciplines.
Questions
- Let #veca=<−2,3># and #vecb =<−5,k>#. Find #k# so that #veca# and #vecb# will be orthogonal. Find k so that →a and →b will be orthogonal?
- What are common mistakes students make with 2-D vectors?
- How do you find the scalar and vector projections of b onto a given #a = ‹3, 2, 1›#, #b = ‹0, 1, 3›#?
- What is meant by the initial point of a vector?
- How do I find the resultant of vectors?
- How can vectors be parallel?
- How do I find the magnitude of a vector?
- How do you write vector U = 6 and Theta = 45 degrees in cartesian form?
- What is the terminal point of a vector?
- How do you find the magnitude and direction for U: magnitude 140, bearing 160° V: magnitude 200, bearing 290°?
- How do you find the scalar and vector projections of b onto a given #a = <3, -6, 2>#, #b = <1, 1, 1>#?
- How do you find the scalar and vector projections of b onto a given #a = i + j + k#, #b = i - j + k#?
- How do you write the vector equation that passes through point (5,7) and parallel to <2,0>?
- How do you write the vector equation that passes through point (-1,4) and parallel to <6,-10>?
- How do you write the vector equation that passes through point (-6,10) and parallel to <3,2>?
- How do you write the vector equation that passes through point (1,5) and parallel to <-7,2>?
- How do you write the vector equation that passes through point (1,0) and parallel to <-2,-4>?
- Are the vectors #u=<1, -2># and #v=<4, 8># parallel, orthogonal, or neither?
- Show that the vectors # 4 bb ul a - 8bb ul b# and #-26bb ul a+52bb ul b # are parallel?
- How to find the linear equation of the plane through the point #(1,2,3)# and contains the line represented by the vector equation #r(t)=⟨3t,6−2t,1−2t⟩# ?