1. Find the distance between p(-2, 3,0) and Q(2,1,5). 2. Find the direction of A = 2i - 3j+7k. 3. Find the angle between A = i-2j+ k and B = 2i - j - k. 4. Prove that A = 8i - 7j+ k and B = 64i - 56j + 8k are parallel.

Q: 5) Find the angle between the lines. y+2 %3D z-5 2x – 3 = y + 9 = 2z + 7 & x +1 = | 2 2.

A: Putting the value of drs of line , we can get angle

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A: Multiply magnitude and unit vector for components

Q: 1. Find a unit vector that has the same direction as the vector (-4, 2,4).

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Let u = (2, -3, 4) and v = (-2, 1, 3). What is the dot product u v? What is the angle between u an v…

A: The given vectors  and

Q: 1. Three vectors are given by: å = 2î – 3ĵ + 5k, b = -2î + 7j – k and č = lî + 2j – 4k. axb Find a,…

A:

Q: Find the cosine of the angle between the planes -3x - 4y – 3z = 3 and the plane - 1x - 3y + 3z = -2.

A:

Q: Find the angle between u = i - 2j - 2k and v = 6i + 3j + 2k.

A:

Q: Find the angle between a and b where -6a+2b=2i+j-8k and 2a-b=3i-4j+k

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Q: Determine whether v = 3i - 5j and w = 6i - 10j are parallel,orthogonal, or neither.

A:

Q: Find an expression for the exact angle 0 between u and v when = (4,7) and v = (-5, 8). (3, –1, 1)…

A:

Q: 8. Consider the vector v = (-7,8) A. What is the angle between = (-7,8) and the positive x-axis? y…

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Q: Let a = (5, — 4) and ☎ = ( − 4, k). - - Find k so that a and will be orthogonal (form a 90 degree…

A: Given thatCondition of vectors orthogonality. Two vectors a and b are orthogonal, if their dot…

Q: If å = 4i + 2j + 4k ,b = -2i + 4j – 3k and ĉ = 4i + 5j. If å + xb is perpendicular to ĉ then find x.

A: Solution:-

Q: Let ä(t) = (5, 4, 2)t + (-6, -4,1) and (u) = (-2, 1, 2)u+ (2, -8,-6). Find the acute angle between…

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Q: 11.[2] Show that vectors A = 4ax - a₂, B = ax + 3ay + 4az, and C = -5ax 3a, 3az form the sides of a…

A: We know that if the vector form sides of triangle then A→+B→+C→=0 Given,…

Q: Find the distance between u and v.u = (−1, 2, 5), v = (3, 0, −1)

A: to find the distance between u and v where u = (−1, 2, 5), v = (3, 0, −1) we use the Euclidean…

Q: -When rotating the triangle (abc) by 30° about the origin, where a-(1,1), b-(4,1) & e-4,3), the new…

A: