4. (a) Find the unit vector that has the same direction as (3,4,0). (a) Calculate the distance between the vectors (1,2,3, 4) and (0,0,0,0).

Q: Find two vectors v1 and v2 whose sum is (-5, –5, 5), where vi is parallel to a =(0, –1, –2) while v2…

A:

Q: Find a unit vector that are orthogonal to the vector (2,−3,1), (5,−2,0), and (3,0,1)

A:

Q: ) Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A: Given problem:- Find the vector that parallel to the intersection line of two planes 2x + y - 3z = 2…

Q: Find a vector equation for the line through the point (-3, –1,8) perpendicular to the vectors ū =…

A: vector equation can be find in the following way:-

Q: Find the vector with length 3 making an angle of 7π/4 with the positive x-axis.

A: Given that the vector with length of 3 makes an angle of 7π/4 with the positive x-axis.

Q: Find a nonzero vector parallel to the line of intersection of the two planes 2y 5x - 3x = -5 and 5y…

A:

Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

A:

Q: Find the shortest distance from point P = (1,2,-3) to the plane which passes through (2,3,-1) and…

A:

Q: A vector orthogonal to the plane through the points (-1,0, 0), (0, 0,-2), (2, 3, 4) is

A:

Q: 1. Find a unit vector that has the same direction as the vector (-4, 2,4).

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 26. Find the vector that has the same direction as (6, 2, -3) but has length 4.

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

A:

Q: Find the vector with length V17 and same direction as = (7,0, -6).

A:

Q: What is the terminal point of the vector a = (2, 2) based at P = (2,4)?

A:

Q: Find a vector of length 5 in the direction opposite that of (3, –2, V3).

A: Let the given vector be              a=3i-2j+3k The vector in the direction opposite to a  is  -a.…

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –2, –2), (2, 3, 4) is

A: Query- Find a vector orthogonal to the plane through the points -1,0,0,0,-2,-2,2,3,4. Answer- Let…

Q: Show that if a particle moves with constant speed, then the velocity and acceleration vectors are…

A:

Q: Find a unit vector that is orthogonal to both [0, 1, 1] and [1, 0, 1].

A: The given vectors are u=(0,1,1) & v=(1,0,1).

Q: Find the equation of the plane containing the point ( – 5, – 10, 9) and the two vectors and -

A: Given that , Plane containing the point -5,-10,9 So , a→=-5 i^-10 j^+9 k^ And vectors are ,…

Q: 8. Find the scalar equation of the line passing through the point (1, 5) that has a normal vector…

A:

Q: how can i learnd about vector in r2 and r3?

A:

Q: Find two unit vectors orthogonal to both (1,-1,1) and (1,0,3)

A:

Q: Find the component form and length of the vector v that has initial point (3, −7) and terminal point…

A: Given: Initial point (3,-7) and terminal point (-2,5).

Q: What is the vector equation of the line segment that connects point P(1,−1,2) to point Q (4,1,7)?

A: Given, A line segment passes through the points P1,-1,2 and Q4,1,7 We have, the vector equation of a…

Q: Find two unit vectors orthogonal to a = (-2, 1, 0) and b = (-4,0, 1)

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: A vector orthogonal to the plane through the points (-1,0,0), (0, –2, -2), (2,3, 4) is

A: A vector orthogonal to the plane through the points (-1,0,0) , (0,-2,-2) , (2,3,4) is

Q: Show that the point 1, - 2, 0 lies on both planes 3x-2y+z=7 and x-4y-2z=9. Hence, find the vector…

A:

Q: Express à = (3, 1, –1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

A:

Q: The vector with terminal point at P(-5,0,3) and initial point at Q(6, 2, –8) is equal to the…

A:

Q: Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A:

Q: The unit vector (1,0,0) is initially on the x-axis. If it is rotated in the positive xz direction by…

A:

Q: Express à = (3, 1, – 1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

A:

Q: 1. The vector in the opposite direction to u = (-1,0) and of half its length is 2. The vector of…

A: 1.The vector is u=<-1,0>2.The vector is v=<-4,5,-3>

Q: 5. Verify that its possible for a line with direction vector J=(2,1,-2) to lie flat on a plane with…

A: The vector equation of a plane is given by the expression . Here, and are the vectors that lie on…

Q: If vector u has initial point (3,0) and terminal point (7,-2), find the linear combination of vector…

A:

Q: Find two unit vectors orthogonal to both (6, 9, 1) and (-1, 1, 0). (vector with the smaller…

A:

Q: Find the unit vector along the line joining point (2, 4, 4) to point ( - 3 , 2, 2). A) -0.8703ax -…

A: We can solve this as follows:

Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

A:

Q: Write down the vector equation of the line that passes through the points (x,y,z) = (2,3,7) and…

A: The given problem is to find the vector equation of line that passes through the given two points.

Q: Find the vector of length 2 making an angle of 45° with the x-axis.

A: Find the vector from the given data

Q: Find a vector u € R' such that, at the point (2, 1, -1), the function f(, v, 2) =-y + 2a2 + has its…

A: Given, f(x,y,z)=-y3+2x2+z2

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, – 1, –2), (2, 3, 4) is

A: This could be solve using vector concept.

Q: Find a unit vector perpendicular to both (3,-2,4) and (-1,2,-3).

A:

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –1, -2), (2, 3, 4) is

A:

Q: Find a vector equation for the line segment from (2, -1, 4) to (4, 6, 1)

A:

Q: Determine the vector equation for the line that is parallel to = [1,5,-7]+[2,-1,5] with the same…

A: The general equation of line in vector form is    .Then note the result : Line passing through the…

Q: Find an equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…

A: Given An equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…

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.