Find the distance bet ween the point of in ter section lines A=:?, 3 -2 and the plane the two %3D and X-6 %3D %3D 2. 2. through the point (21314) the vector i-uj43k that Passes and is perpendicular to

Q: A line L has a direction vector v =i+3j+ V6k and passes through the point Q. Find the distance…

A:

Q: Use the vectors shown to sketch u - 3v. (Assume that each point lies on the grid lines and that each…

A: Sketch the vector:  First draw the vector 3v: For -3v, the vector will change its direction.

Q: Let A and B be two points with position vectors A and B, respectively. Show that the line passing…

A: To derive the vector form of the required straight line

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

A: According to the vector midpoint formula: Where 'c' is the midpoint position vector of vector 'a'…

Q: 10. In the figure here, D is the midpoint of side AB of triangle ABC, and E is one-third of the way…

A:

Q: The position vectors of points A, B and C are OÃ = 2i – j + nk , OB =ỉ+3j – 2K and OC = -i – mỉ – 3k…

A:

Q: In the figure here, D is the midpoint of side AB of triangle ABC, and E is one-third of the way…

A: Consider the figure shown belowAssume , D is the midpoint of side AB of triangle ABC , and E is…

Q: Find the distance of point A(23.2) from the line that passes through the origin and parallel to the…

A: given point A 23 ,2 and line passes through orgin and parallel to the vector v =<1,3>

Q: The position vectors of points A, B and C are OA = 21 -j + nk , OB=i+ 3j – 2k and OC = -i - mj – 3k…

A:

Q: Verify that 2j+k is perpendicular to the plane I7, Find a vector perpendicular to the plane II, Find…

A: Given that the plane Π2 contains the point O, A and B and the plane Π3 contains the points O, A and…

Q: tind the component form of the given vector V. belaw Dont forget round off to two decimal places.…

A:

Q: The three vertices of a triangle are located at A(6,-1,2), B(-2,3,-4), area of the triangle; (c) a…

A:

Q: The position vectors of points A, B and C are OA = 2ỉ -j + nk , OB =i+ 3j – 2k and OC = -i- mj – 3K…

A:

Q: Find the measures of the angles of the triangle where vertices are A =(-1,0), (2,1), C = (1,-20).…

A: The given triangle will be

Q: 5. Consider two vectors (a) Find the vector normal to (b) Find the plane through and = 27+77 and…

A:

Q: 14. The accompanying figure shows nonzero vectors v, w, and z, with z orthogonal to the line L, and…

A: Given V and W make any equal angle with L. |v| = |w| Z and L are orthogonal to each other.

Q: Find the measure of the smallest nonnegative angle between the two vectors. Round approximate…

A:

Q: Two vectors of magnitudes B= 5 and C = 3 are lying on the xy plane as shown in the figure. What is…

A:

Q: Construct the vectors a = 3k - 2j and b = 3i - 2j and c = ax b. Compute the absolute value of the…

A: Given data : a⇀=3k-2jb⇀=3i-2j To calculate c=a×b The value a×b=ijk0-233-20

Q: A) Find the angle between the vectors u = 21 +j+9k, v = 61-12j and %3D sketch the vectors and the…

A: Given,u=2i+j+9kv=6i-12jWe know that cosθ=|u.v|u||v||u.v=(2i+j+9k)(6i-12j)u.v=12-12u.v=0Therefore…

Q: Given the points P (1, 2, 2), Q (2, -1, 4), R (3, 5, -2) and S(0,-1,3). (a) Use vectors to calculate…

A:

Q: 1. Let p, be the vector in R? which is obtained by rotating the point about the origin through an…

A: The position of the object can be determined by using either cartesian or polar coordinates. The…

Q: Consider a triangular pyramid ABCD the position vector of whose angular points are A(3,0, 1) B(-L…

A: Given data: The given position vector of A is (x1 y1 z1)= (3,0,1). The given position vector of B is…

Q: A. plane is flying miles per With and heading of 146- TF unning at 4 miles per hour Currents are r…

A: Given: Airspeed 160miles/hour, heading 140∘Wind speed 41mi/hr, headeing 155∘

Q: Consider the regular octagon centered at the origin as shown at right. Eight unit vectors are drawn…

A: By definition, the cross product of two vectors is a vector in the direction perpendicular to the…

Q: 16. The accompanying figure shows nonzero vectors v, w, and z, with z orthogonal to the line L, and…

A:

Q: a. Which translation vector represents the path of the ball from T tol DC? DC? b. What translation…

A: GIVEN :

Q: A) Find the angle between the vectors u 21+j+ 9k,v 61-12j and %3D sketch the vectors and the angle…

A:

Q: Find the median AD of the triangle ABC where positive vectors of the vertices A, B and C are…

A: Vertices of the Triangle ABC given A=i+j,B=4i+6j,C=i-j; Hence, We can take these vectors as the…

Q: Let a =)33) A) Find the eavution of the Plane which has a a nomal vector t conthins Point 3,3) Find…

A: To solve this problem we use here the definition of a plane passing through a given point and…

Q: Q3. Prove that (only one): a-dy is a unit vector? a- %3! b- L = 6a, - 3a, + 2a, and M = 3a, + 2a, -…

A: Topic- Vector

Q: e) Four non-coplanar points A, B, C, D are positioned such that the line AB is perpendicular to CD,…

A:

Q: The position vectors of A and B with respect to the origin O are a and b respectively. M is the…

A:

Q: Find parametric equations for the lines in The line through (2, 3, 0) perpendicular to the vectors u…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: 1Triangte with points (2.0r-)ornd R(or2 find -Ared of the iangle 7 vector PerPend teular to 2 AUnit…

A:

Q: The line / passes through the points with position vectors 2i – 3j + 5k and 7j + k. Given the point…

A: Given points are (2,-3,5) and (0,7,1)  So the direction ratio of the line= (2,-3,5) - (0,7,1)=…

Q: Q1:A-Find the equation of plane passes through (0,2,-1) parallel to the plane 3x+y+z=7? b- Find…

A: 1. A. According to question,Given plane,3x+y+z=7,Given Point 0, 2, -1

Q: The position vectors of points A, B and C are OA = 21 -j + nk, OB =i+ 3j – 2k and oc = -i- mj – 3k ,…

A:

Q: The position vectors of A and B with respect to the origin O are a and b respectively. M is the…

A: Given that position vector of A and B with respect to the origin O are a and b respectively. M is…

Q: Two vectors are given as A=-1a, + 6a, + 6a, B=-6a, + 5a, + 6a, Find a unit vector normal to the…

A: Given,Two vectors are-A=-1ax+6ay+6azB=-6ax+5ay+6az

Q: Points A, B and C are defined by position vectors 2i – j – 4k, –i +j+2k and i – 3j– 2k respectively.…

A:

Q: )P=(3,2,1), then the parametric equation of the line is :   a.

A:

Q: Determine two unit vectors, vand wl, perpendicular to the plane passing through the z-axis and point…

A:

Q: ABCD is a parallelogram, where A, B and C have position vectors i + 2j – k, 2i + j- 2k and 4i – k…

A:

Q: Q Find the distance bet ween the point of lines Xa = =, and the plane in ter section the two %3D 3.…

A: Given lines:

Q: A line L has a direction vector v = i+ 3j+ V6k and passes through the point Q. Find the distance…

A:

Q: ABCD is a parallelogram with diagonals AC and BD that intersect at E. Assuming the properties of a…

A:

Q: 3-a. Find the area of the triangle determined by the points P, Q, and R. b. Find a unit vector…

A: Given points P(1,-1,2)  Q(2,0,-1)  R(0,2,-1) (a) The objective is to find the area of the triangle…