ā − Let a = <3, 1, 5 > and b = < 4, 5, k>. - Find k so that a and b will be orthogonal (form a 90 degree angle). k=

Q: The figure was translated 1 unit left and 10 units down, then rotated 90 counterclockwise. If B"(-2,…

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Q: Find the cross product a × b where a = (0, 3, 4) and b = (5,1,2). axb =

A: Step 1: Step 2: Step 3: Step 4:

Q: 23. Given v4 = 7i - 3j and v5 = i +4j. Simplify the following. V4 + 4V5 a. (-11, 19) b. (11,-19) c.…

A: We are given that      V4 = 7i - 3j     V5 = i + 4j we need to find    V4 + 4V5 .

Q: 39. Given a = (3, -4) and b = (1, 2). Find the vector 2 a. (3,4) a. b. 2,4) c. (6,-8) d. (5,-2)

A: From the given statement,

Q: OLet U=(2,-37, V=Fl,5), W=(4,-62 Find U•V

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Q: Find the angle between the two planes. The first plane contains the points A(1,2,3), B(6,3,2),…

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Q: 02. Given the vectors : A = (3.-1, 2), B = (0, 1, 1) and C- (2, 2,-1), find: the angles between the…

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Q: Let U=(-4, 3, 3) and V=(2, 1, 1). Find (2U+V), *. | (then find | (2U+V

A: Find 2U+V and it's magnitude.

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

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Q: B=(-83,57) 6-(27,-50) and D (30,51) 4. Points 0, A= (-79,-49), %3D calculate AB + B Ć t CD

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Q: Determine whether v = -2i + 3j, w = -6i - 9j are parallel, orthogonal, or neither.

A: Determine whether v=-2i+3j,  w=-6i-9j are parallel, orthogonal, or neither. Solution:- if two…

Q: 40. Given a = (3,-4) and b = (1, 2). Find the vector a + 2b a. (5,-8) b.(5,0) c.(4,-4) d. (4,0)

A: Given,

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: 3. the dot product of -

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Q: Suppose u = (-3,0,0) and v = (-3,-2,3). Then: u +0= u – T= | 3u= 7u – 30=

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Q: Determine the angle between the lines AB and AC delimited by the points A(4,3,2), B(6,1,-2),…

A: Step 1:  Step 2: Step 3: Step 4:

Q: Find the area of the parallelogram whose vertices are: A(0,0,0) B(5,2,6) C(9,-1,6) D(4,-3,0)

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Q: the distance between A and B •the distance between A and C

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Q: Find the area of the parallelogram with vertices: P(0,0,0), Q(-4,-5,4), R(-4,-3,6), S(-8,-8,10). 0

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Q: Q3/ Give a pictorial view for the points to show its position in space: we this A-2,-4) ,B=(4,0) ,…

A: The first point A= (-2,-4) lies in the third quadrant, the second point B= (4,0) lies in first…

Q: For the vectors a = &lt;2, 8&gt; and b = &lt;4, 6&gt;    find orthab.

A: The objective of the question is to find the orthogonal projection of vector a onto vector b. The…