The position vectors of the points A and B are given by a = 2i + 3j and b = 4i + j respectively. Write down a vector equation of the line AB and find the value of α if the point C with position vector c = 7 i + α j lies on AB

Q: 12 If the position vectors of P and Q are i+3j- 7k and 5i - 2j + 4k respectively, find PQ and…

A: Since,you have posted multiple questions so according to our guidelines we will solve only first…

Q: If a and b denote the vectors OA and OB, indicate on the same diagram the vectors OC and OD denoted…

A: As first question and second question are independent so I am solving only first question.If you…

Q: The current of a river is given by the vector (7,5). The direction of the vector is

A: We have to find the direction

Q: The vector equation for the line segment that joins the point P(1, 3, –2) to the point Q(2, – 1, 3)…

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

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Q: Express the given vector in terms of the unit vectors i, j, and k. (2, -5, 0)

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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: a = 8i-j+ 4k, , b=4j + 2k Find the angle between the vectors.( First find an exact expression and…

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Q: The unit vector from the origin to the point A is given as (6, -2, -4), and the unit vector from the…

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

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Q: Given initial point  P1 = (−2, 1)  and terminal point  P2 = (5, 4),  write the vector v in terms…

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Q: When analyzing the vector To the sum of two vectors, the first is parallel to the vector A = 2i-i+3k…

A: There is no specific formula.Please go through the solution.

Q: Draw the vector V that goes from the origin to the given point. Then write V in terms ofthe unit…

A: We have to draw a vector that starts from the origin (0,0) and goes to the point (-1,-5).

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: Given the points A(1,2,3,) and B(2,-2,1) Find the Vectors A and B with respect to origin. Unit…

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Q: Give two vectors A=4i+3j, B=5i-2j Find its values and the direction of vector C, which is 2A-B

A: Vector addition

Q: The position vectors of points P and Q are i+2j-k and 7i+ 3j-4k respectively. (a) Find a vector…

A: Given problem:- The position vectors of points P and Q are i+2j-k and 7i+3j-4k respectively. (a)…

Q: Given initial point P1 = (-2, 3) and terminal point P2 = (6, 5), write the vector v in terms of i…

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Q: Draw the vector V that goes from the origin to the given point. (3, -4) y -6 -4 -12 2 -4 -2 -2 -4 y…

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Q: 1. Find the position vector of the point of intersection of the line joining the points whose…

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

Q: The points A, B, C and D form a parallelogram. The points A, B and C have position vectors 2i –…

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j…

A: a)a→=-3 i + 8 jUnit vector as the same direction;u= a→a→ =(-3 i + 8 j)(-3)2+(8)2u=(-3 i + 8…

Q: 12. If the position vectors of P and Q are i + 3j-7k and 5i- 2j + 4k respectively, find PQ and…

A: NOTE: Hi! Thank you for your question. As per the honor code we are allowed to answer one question…

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

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Q: Given initial point P1 = (6, 6) and terminal point P2 = (−6, 6), write the vector v in terms…

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Q: If a and b are two non-parallel vectors and the position vectors of P, Q and R are a + 2b, 1/2a +…

A: answer

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: If a = 31 - j-4k, b= - 2i + 4j- 3k and c =i+ 2j-k. Find unit vector parallel to 3 a -2 b +4 c Find…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Draw the vector V that goes from the origin to the given point. Then write V in terms ofthe unit…

A: To draw the vector V from origin

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: Given initial point  P1 = (2, 5) and terminal point P2 = (−1, 6),write the vector v in terms of i…

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j…

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Q: The point A has position vector i+5k and the line l1 has vector equation r=7i+4j–2k+ a(5i+3j+k). (a)…

A: The position vector of point A is given by i+5k. The line l1 has vector equation…

Q: Find a unit vector that has the same direction as the given vector. −4i + 3j − k

A: The objective is to find a unit vector that has the same direction as the given vector. −4i + 3j −…

Q: The points A and B have position vectors j+2k and 2i+j-2k respectively. (i) Find a vector equation…

A: Since solve the first question for you. If you want any specific question to be solved then please…

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: Find the component form of the vector v if ||v|| = 5 and when drawn in the standard position v ties…

A: Given: ||v|| = 5  θ=45∘

Q: 1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 1 3, a +2b,…

A: The equation of the line PQ is : PQ=Q-P=12a+34b-(a+2b)=12a+34b-a-2b=-12a-54b The equation of the…

Q: Find two unit vectors in 2-space that make an angle of 45° with 6i + 5j. Enter the vector i as i,…

A: here here we have

Q: Gandalf the grey started in the forest of Mirkwood at a point with coordinates (3, -1) and arrived…

A: In the question we have to find the co-ordinates where Gandalf will make turn.

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

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Q: A line L has a direction vector v = 2i + i + 2k and passes through the point Q. Find the distance…

A: Consider the following figure Given QP→×v=18 and v=2i^+j^+2k^ We have to find the distance d which…

Q: Sketch the vectors ro = and v= and then sketch the six vectors ro±v,ro ± 2v,ro± 3v. Draw the line L:…

A: Given the vectors r0=-1,2 and v=1,1. The objective is to compute the vectors r0±v, r0±2v and r0±3v…

Q: Find a unit vector that has the same direction as the given vector. 2i − j + 2k

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j…

A: Since you have asked multiple questions in a single request we would be answering only the first…

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: If a = 3i-j-4k, b - 2i + 4j-3k and c i+2j-k. Find unit vector parallel to 3 a -2 b +4 c. Q.1

A: Comment:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: If a vector V is in standard position and the tip of the vector corresponds to the point(a, b), then…

A: Given, If a vector V is in standard position and the tip of the vector corresponds to the point(a,…