a) Find vector equation and paramedrie equahion for the line that passes through the point (5,1,3) and is parallel to the vector ituj-2k.

Q: Show that the vectors i - j, j - k, k - i are parallel to a plane.

A:

Q: Define the term Parallel Vectors?

A: Parallel vectors: The vectors that are parallel if they have the same direction.

Q: Find a unit vector perpen dicular to the plane of the vectors a = (2, -3,1) and b = (1, 2, -4)

A:

Q: Find two unit vectors that are normal to the plane determined by the points A (0, –1, 2),B (1,…

A: To find the two-unit vectors that are normal to the plane determine by the given points.

Q: Find the unit vector that has the same direction as vector v that begins at (1, 4, 10) and ends at…

A: We will find the unit vector that has the same direction with the given vector v in the following…

Q: Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a rectangular…

A: Question- Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a…

Q: Find a vector equation with parameter t for the line through the points (–1, –7, –4) and (-9, 8, 2).

A: we know that vector equation of line which passes through pointsx1,y1,z1,x2,y2,z2 is given by…

Q: Find the vector of length 2 making an angle of 60° with the x-axis.

A:

Q: Find the distance from the origin to the plane through the point (-6,3, -2) and having 5i - 3j° + 4k…

A:

Q: If vector a= and vector b= are vectors a and b orthogonal, parallel, or neither? Provide

A:

Q: Define the points P(-4, 1), Q(3, -4), and R(2, 6).

A: The given points are The vector QP is So, the unit vector (v) of QP is

Q: A three-dimensional unit vector parallel to the y-axis is

A:

Q: The sum of the squares of the direction cosines of a vector in space add up to ..............

A:

Q: Determine the equations of the line (vector, parametric, Cartesian and general) that passes through…

A:

Q: Find the terminal point of a vector of magnitude 5 that is parallel to the vector 1, 2, 3 and whose…

A: We will first find direction of vector using the magnitude and values of initial point and parallel…

Q: Find the length of the vector a %3D

A: The length of a vector x→=abc is given by the equation; ||x→||=a2+b2+c2

Q: The plane contains the point (2, −1, 6) and is normal to the vector <2, −1, 6>.

A: Given: A plane passes through the point 2, -1, 6 and normal to the vector 2i^-j^+6k^.

Q: Consider points P(3, 0, 2) and Q(-1, -1, 4). (a) Express vector PQ with the initial point at Pand…

A:

Q: A vector is in standard position if the _____ of the vector is placed at the ______ ofa rectangular…

A: To fill up the blanks,  A vector is in standard position if the _____ of the vector is placed at the…

Q: Is the pair of vectors 2i – j and -i+jperpendicular? no yes

A: Given vectors 2i-j and -i+j Two vectors are perpendicular if and only if dot product of those two…

Q: Given a vector with initial point (−8, 3) and terminal point (5, −5), find an equivalent vector…

A: In the question we have to find an equivalent vector with initial points (0,0).

Q: 3 Determine the unit vectors that are nernendicular to A - and R -

A: Perpendicular vectors

Q: 2. Convert the vector A=10ax in the Cartesian Coordinates into a vector expressed in the Cylindrical…

A:

Q: Find the distance of point 4(2/3,2) from the line that passes through the origin and parallel to the…

A: follow next step

Q: Find the vector of length v7 in the direction of AB + AC

A:

Q: Find two different vector parametrizations of the line through P = (5, 5, 2) with direction vector v…

A: Given the points are (5,5,2) and the direction vector v=<0,-2,1>Hence, Vector…

Q: Use vectors to prove that the line segment joining the midpoints of two sides of a triangle is…

A: Using Vectors, Our Aim is to prove that the line segment joining the midpoints of two sides of a…

Q: Show that the vectors 3 do not span R° by giving a vector not in their span.

A:

Q: Use vectors to prove that the line connecting the midpoints of two sides of a triangle is parallel…

A: Let the arbitrary triangle has vertices A, B and C has three vectors AB, →AC →  and  BC → . Let M…

Q: Find an equation of the plane through the point (29,-37,46) and with normal vector 14i+19j–17k.

A: we have to find an equation of the plane passing through the point (29,-37,46) and with normal…

Q: Find the distance of point 4(2-/3,2) from the line that passes through the origin and parallel to…

A: Distance of a point A(x1, y1) from the line ax+by+c=0 is given by d=ax1+by1+ca2+b2

Q: Find a vector of length 3 pointing in the same direction as .

A: Find a vector of length 3 pointing in the same direction as 4,-3,-4

Q: 4. Determine a vector equation for the plane that is parallel to the xy -plane and passes through…

A: Due to our answering guidelines we can only answer one question at a time, therefore I will be…

Q: 3. Compute the angle between vector a = (1,2,3) and the positive r-axis.

A:

Q: | Show that the vectors 2 do not span R³ by giving a vector not in their span.

A:

Q: Show that the vectors do not span R' by giving a vector not in their span.

A: Solution :-

Q: a. Find a unit vector perpendicular to the plane of P (4,2,1), Q (1,2,0), R (1,1,2). Whereas P is a…

A: Due to Bartleby guidelines, only 1question can be solved. Please repost the remaining questions to…

Q: Prove that the points position vectors collinear. With at 26, 2a-5 and 3a-46 are

A:

Q: tind a non-zero vector perpendıcular to the vectar u. Find the length of the vector R-

A: Consider two vector u→=ai→+bj→ and v→=ci→+dj→ if the two vector is perpendicular then the angle…

Q: Use vectors to prove that the line joining the midpoints of two sides of a triangle is parallel to…

A:

Q: Express the vector v with initial point P and terminal point Q in component form. (Assume that each…

A: From the graph we can se that the coordinates of point P is 5, 2 and the coordinates of point Q is…

Q: Find a unit vector perpendicular to plane PQR. Р(1, -1, 2), Q(2, 0, — 1), R(0, 2, 1)

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the component form and magnitude of vector v. 7. Initial Point (12,-3) Terminal Point (4,-1)

A: We can find the answer as below

Q: Give a vector description of the midpoint M of a line segment AB→.

A: GivenLine segment AB→To find vector description of midpoint of AB

Q: find the component form of the vector. The unit vector obtained by rotating the vector [0, 1]…

A: Given unit vector is 0,1 makes an angle of 90°. The vector obtained by rotating it by 120° counter…

Q: Express the vector v with initial point P and terminal point Q in component form. (Assume that each…

A:

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.