1. Find the position vector of the point of intersection of the line joining the points whose position vectors are 5i − 4j and −3i + 4j with the line joining the points whose position vectors are −13i + 4j and −5i + j.

Q: и Match the vectors p, q, r, s, and t with one of the combinations of the u and v vectors from the…

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Q: bäi The cross product of the vectors 3ax + 4ay – 5az and -ax + ay - 2az * ,is -3ax+11ay-7az O -3ax +…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Q6) if A=2i-3j+4k, B=-i+2j+5k and C= 3i+6j-k, Find the indicated scalar or vector : 1) 2) A-(Ã+B +…

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Q: Find the vector equation of the line that passes through (1,0,-3) and it's parallel to v=2i - 4j +…

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Q: 35. The position vectors of the points A and B are OA =2i + j- 4k,OB =-2i +4 j – 2k , a vector…

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Q: Find the angle between the vectors ū = 5i – 5j +k and v = 2i + 16k.

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: 2. The two unit vectors parallel to the line 3x + 4y = 1 are and 3. The two unit vectors…

A: 2) The line is 3x+4y=1. Rewrite the equation of the line in the slope intercept form as,…

Q: find the component form of the vector. The sum of AB and CD, where A = (1, -1), B = (2, 0), C = (-1,…

A: Given that A = (1, -1), B = (2, 0), C = (-1, 3), and D = (-2, 2)We have to find AB + CD.

Q: 13. Show that the pair of vectors i + i and i – i is perpendicular.

A: Two vectors is said to be perpendicular if their scalar product is zero.

Q: 4. Find the vector equations for the line of intersection of the following planes: 2x – y – 5z = -14…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: We have to find the equation of plane.

Q: 2 Describe each of the translations shown using column vectors. a d e 3 Using the vectors in…

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Q: Find the equation of the plane through the point with position vector 5i-2j+3k perpendicular to the…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: The equation of the plane P which is normal to the vector n and passes through the point R is given…

Q: If u.v.w are three vectors such that each is inclined at an angle of " with the other two, and that…

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Q: 1. Assume the lengths of the vectors 2a – b and a + 3b , assuming a = (2,1,3) and b = (-1,2,2)

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

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Topic = Geometry

Q: ) Write down the position vectors of any two points on the line T·(3i – 4j)+ 2 = 0 and hence find…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Match the vectors p, q, 7, s, and t with one of the combinations of the u and i vectors from the…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: The position vectors of the points A and B are given by a = 2i+3j and b = 4i+j respectively. Write…

A: Given that: Position vectors of A and B are:        a=2i+3j        b=4i+j

Q: Find the angle between the vectors a 0 = and b = 2i+j - 4k. 10i - j - 5k

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Q: Given two vectors A = 2i + 3j- 2k B = 3i- 4j- 6k Determine the vector that defines the direction of…

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Q: Find the equation of the plane passes through the point P(4,2,1) and perpendicular to the vector…

A: Equation of the plane passing through point P(x0,y0,z0) on the plane and perpendicular to the vector…

Q: 1. Use the vectors in the figure at the right to graph each of the following vectors on the plane…

A: Draw the correct vectors 2v & -3w than form the triangle sum.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Consider the vectors a= 2i +4j-6k, b*=-31 +k and c = 3j¯- 2k. Find a un vector parallel to - 2a…

A: Given query is to find the indicated unit vector.

Q: 36) Find the values of x and So the vectors 2i+3 and xi +4j are equal.

A: Two vector are equal if and only if their magnitude are equal and have same direction.

Q: 1. The two unit vectors parallel to the line y = 2x 1 are | and 2. The two unit vectors parallel to…

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Q: Let v = -5i + 2j and w = 2i - 4j. Find the specified vector, scalar, or angle 3v - 4w.

A: Let v = -5i + 2j and w = 2i - 4j. Find the specified vector, scalar, or angle 3v - 4w.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: 13. Given the points A(3,5) and B( – 3, – 7), find a. the vector equation of the line.

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Q: Q3 - A//Find the value of M such that the vectors A 2i+ Mj+k and B = 4i-2j-2k %3D are perpendicular…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Here, the required plane is perpendicular to the vector n=-2i+8k.

Q: (B): Find the unit vector 3i - 4j + 5k perpendicular to the vectors: 4i + 5j-6k

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Q: га- Find an equation that describes all values of a, b, and c for which the vector w = |b| is NOT a…

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Q: A = x6- y9+z3 B = x6- y3+z9 C = x 2- yl-zl For the given vectors A,B, and C show that whether C is…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Explanation of the answer is as follows

Q: Find the position vector of the point of intersection of the line joining the points whose position…

A: Given: The position vector of the points 5i^-4j^ and -3i^+4j^; -13i^+4j^ and -5i^+j^

Q: Determine the vector 8a – 7b if a = -3i + 2j – 4k and b = 5i + 6j + 2k. 8a – 7b help (vectors)

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Q: 4.14. Determine whether vectors u and v are orthogonal, parallel, or neither for u =i and v = -2i+…

A: You need to verify by using orthogonal and parallel test of two vectors using their dot product.

Q: 1. The two unit vectors parallel to the line y 5x + 2 are and 2. The two unit vectors parallel to…

A: 1. Put x=t, then y=5t+2 and the parametric equation of the line is rt=t,5t+2=0,2+t1,5 and parallel…

Q: 11.3.19 In the figure to the right, it looks as if v, + v, and v, - v, are orthogonal. Under what…

A: Dot product of two orthogonal vectors are always equals to "0" . Therefore, if v1+v2 and v1-v2 are…

Q: Find the vector equation of a line L going through the point P = (-5, -6) and parallel to the line…

A: The vector equation of line is

Q: When decomposing the vector into the sum of two vectors, the first is parallel to the vector A = 2i…

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Q: 2 A plane is flying on a course of 060° in still air at a speed of 300 km hr-', when it passes a…

A: Given that: Speed of plane = 300 km hr-1 Direction = Course of 60o