The distance from point A(8,-6, 3) to the line L: x=-2-6t, y=9-6t, z = 9+5t is: Hint: The distance from a point A to the line passing through point P and parallel to the vector v is given by: PAX V 09 O 19 O 22 O 15 O 11 d= PI V

Q: Find a unit vector in the same direction as v= (28,-21).

A: A unit vector in the direction of (a, b)

Q: Consider the points P(5, −2, 3) and q(−3, 0, 2) a. Write vector |op| using unit vectors. b. Write…

A: Basics of VECTOR are used.

Q: If A = 4a, - 6a, + a, and B = 2a, + 5a,, find: (a) A B +2|B (b) a unit vector perpendicular to both…

A:

Q: Let vector v = 3i – 2j+ 4k and point P = (0,0, -3). For what point Q is it true that v = PQ?

A:

Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: For two vectors A and B, what is the value of A X B²+ (A.B)²?

A:

Q: Determine the dot product for the two vectors: x = ai+bj+ck and y = di+ej+fk where a = 4, b = 5, c =…

A: Given,

Q: 1 - x 1 2 - y = z +1 and l2 : х — Consider the lines l1 : = y – 2 = 3 || 2.

A:

Q: Show that direction vectors of the lines 3 L: and

A: We have to find the direction vectors for the lines L1: x-32=y+14=z-2-1 and L2: x-35=y+1-2=z-32.

Q: Find the angle between lines AB and AC where the point A(4,4,1), the point B(−4,7,7), and the point…

A:

Q: Which of the following pairs of vectors are perpendicular? -/2 > and O A | -12 > and OB. - 2/2 >…

A: We need to find the pair of vectors which are perpendicular. This can be done as follows:

Q: For unit vectors v and w, find the dot products of: v and -v: v+w and vw: v+2w and v2w: 1v2w and lv…

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Q: Given vectors u = <-3, -7> and v = <-1, 5>, find the resultant vector  u + v.

A: The objective of this question is to find the resultant vector when two given vectors are added…

Q: A point A(-5,-3) is translated by the vector v = , and then reflected about the line y=0. the…

A: Given that: A(-5, -3) is translated by v=<8, 0>

Q: find an equationfor the line through P parallel to v. Then sketch the line. Include v inyour sketch…

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

Q: v= (-8,-6) and w=(-12,5) Find the following given: 3v – 2w = а. +w = с. Find the unit vector having…

A: This question is related to vectors, We will solve it using given information.

Q: Given the points A: (-6,6,-5) and B: (3,-1,0), find the vector i AB i = <

A: Since, we have been given the points A (-6,-6, 5) and B(3,-1, 0).Our Aim is to find the vector u⇀…

Q: Find the position vector (i.e. the direction vector) from the point P(−4,−6,3) to the point…

A: To find the position vector (i.e. the direction vector) from the point  P-4, -6, 3 to the point Q4,…

Q: Q5) Given points A (10, -3, 4) and B(-4, 3, 5), find: a. The distance from A to B. b. A unit vector…

A:

Q: Find the direction of v:v =(7,-2)

A: Given: v→=7,-2

Q: 3) Find equations for the lines: a. The line through the point P(3,-4,-1) parallel to the vector…

A: Here we have to find the equations for the lines,  a) The line through the point P(3,-4,-1) and…