c) The vector from the origin to the point A is given as (6, -2, -4), and the unit vector directed from the origin toward point B is (2, -2, 1)/3. If points A and B are 10 units apart, calculate the coordinates of point B.

Q: The vector from the origin to point A is given as (-2, 3, 5) and the unit vector directed from the…

A: A = (-2, 3, 5)  Thus, position vector of A,  a =  -2ax + 3ay + 5az   UB  =  0.535ax + 0.802ay -…

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

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Q: Determine the resultant of two vectors with magnitudes of 50 and 30 and an angle of 110 degrees…

A: let  A=50 & B=30, θ=1100 We know resultant between two vectors A→ & B→ when angle between…

Q: If vector a= and vector b=, find the angle between vectors a and b, rounded to the nearest degree.

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Q: If the magnitude of vector x is 10, y is 21 and magnitude of x-y is 17 what would x+y be?

A: Use the property of magnitudes to solve this problem.

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

A:

Q: Determine the unit vector along the direction OP, where O is the origin and P is point (4, –5, 1).

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Q: The path C to D is consistent with what unit vector and its sign? The path G to C is consistent with…

A: Given:  To find the unit vector for the following paths for which they are consistent and the sign…

Q: For the three vectors a, band, it is found that ax statement below is true?

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

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Q: What position vector is equal to the vector from (3, 5, -2) to (0, -6, 3)?

A: We have given two vectors;  (3, 5, -2) , (0, -6, 3)

Q: The vector from the origin to point A is given as 6a, – 2a, - 4a., and the unit vector directed from…

A: Vector A is <6,-2,-4> Let Vector B i s <23B,-23B,13B> The distance between A  and B  are…

Q: 5. Determine the resultant of two vectors with magnitudes of 30 and 70 units and an angle of 45…

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

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Q: Let a and b be two vectors such that Jal =17, b is a unit vector, and 0= " is the angle between…

A: Solve for

Q: The angle formed by placing a vector of length 12 tail-to-tail with the vector [0,2] is 80 degrees.…

A:

Q: α, β and γ are the angles made by the vector with x, y and z axis respectively. The squares of the…

A: Given ,  α, β and γ are the angles made by the vector with x, y and z axisrespectively. We have to…

Q: Show that if u+ v and u - v are orthogonal, then the two vectors must have the same length. What…

A: Hence the two vector u and v have same length.

Q: Finally, verify that the vectors satisfy the Parallelogram Law |||² + ||||? 3. ī = (2, –1), w =…

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Q: The intersection of the two planes given by the vector equations ()- -2 =0 r. and -4 = 3 r. is

A:

Q: Find the measure of the angle between the three-dimensional vectors a and b. Express the answer in…

A: SOLUTION: given vector a=19, -1, 4 and b=1, -1, -5 to find angle between two vectors lets use dot…

Q: the angle made by vector A = 2 ax- ay +2 az and X-axis

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Q: Find the vector pointing in the direction opposite that of (6, –8) with length 20.

A: The given vector  6,-8 For a given vector v, to find a unit vector u in opposite direction of v…

Q: The vector from the origin to point A is given as (-2, -4, 5) and the unit vector directed from the…

A:

Q: The vector having (magnitude) only is called unit vector FO

A: GivenStatement:The vector having only magnitude is called unit vectorTo determineGiven statement is…

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: 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: If v and w are two vectors in standard position (that is with the tail at the origin) in R", then…

A: The given statement is: If v→ and w→ are two vectors in standard position ( that is with the tail at…

Q: Find a unit vector perpendicular to the plane ABC if A (2,-2,1), B (3,-1,2) and C (3,-1,1)?

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Q: Find the angle between the vectors (2, 1) and (3, -2) to the neareast second.

A:

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: The volume of the parallel pipe formed by three vectors A, B, and C is 50 cubic units. if A(-2,6,3),…

A:

Q: 2. The unit vector in the same direction as (-6, 12) is

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Q: The vector from the origin to point A is given as 6ax – 2a, – 4az, and the unit vector directed from…

A: Given vector is A→=6,−2,−4 and B→=B23,−23,13 And B−A=10 We have to find the coordinates of the point…

Q: Express the vectors in terms of their lengths anddirections. -i - j

A: Given vector is: v = -i -j Then we get, The magnitude or the length is: = sqrt{(-1)^2+(-1)^2} =…

Q: What is the size of the angle between the vectors a = (2, 5, -1) and b = (-3, 2, 6)?

A: Given  a = (2, 5, -1) and b = (-3, 2, 6) To find angle between two vectors:

Q: 3. A rocket is fired at an angle of 25° to the ground with an initial velocity of 120mls.Resolve the…

A: The velocity vector can be represented by v→=vxi→+vyj→, where vx and vy are the horizontal and the…

Q: The vector from the origin to point A is given as 6ax – 2a, – 4a-, and t unit vector directed from…

A:

Q: A vector is described as "A quarterback releases a football with a speed of 44 feet per second at an…

A: Given: A quarterback releases a football with a speed of 44 feet per second at an angle of 30° with…

Q: A quarterback releases a football with a speed of 44 feet per second at an angle of 30° with the…

A: θ=30°,  speed=v=44

Q: By finding the dot product for each pair of vectors determine if they are perpendicular: (1,2) and…

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Q: What is the angle in degrees between the two vectors (2, 4. -1) and (4, 8, -2)? Note that the…

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Q: Which of these vectors is equivalent to the vector that has initial point (5,-2) and terminal point…

A: We have to find which of these vectors is equivalent to the vector that has the initial point (5,-2)…

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,…

Q: 4. Find a unit vector that is perpendicular (5, 6). to

A: