The dot product of two vectors Y1 Y2 and j = Yn in R" is defined by a · j = x11 + x2y2 + ...+ x„Yn- The vectors a and j are called perpendicular if a · y = 0. Any vector in R perpendicular to can be written in the form s+ t.

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: express vector as a product of its length and direction. 1/(3)^1/2 i + 1/(3)^1/2 j + 1/(3)^1/2 k

A: Let the given vector is: v=13i+13j+13k

Q: the vectors î+ cos - cos (ß- α) } + cos (y - α) k, cos (a − B) i + j + cos (y – B) k i + cos (B-y)…

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Q: Find a non-zero vector that is orthogonal to (-7,6,5).   Separate your entries by commas, and…

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Q: Explain “ some combination gives the zero vector, other than the trivial combination with every…

A: The statement is “ some combination gives the zero vector, other than the trivial combination with…

Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

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Q: Suppose that u and v are vectors in 3-space such that u ||= 5 and u · v= 7. Find: (a) u · u = (b) v…

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Q: Let u= and v=. Give two vectors that are perpendicular to both u and v.

A: Consider the vectors

Q: How did you get the vectors and to get a cross product for a perpendicular vector to i+j and j+k.

A: How did you get the vectors <1,1,0> and <0,1,1> to get a cross product for a…

Q: Let u = (1, 2, 3), v = (2, 2, -1), and w = (4, 0, -4). Find 2u + 3v - w. STEP 1: Multiply each…

A: Given that the vectors u=1,2,3v=2,2,-1w=4,0,-4    .

Q: Find the equation for the plane through the point Po = (2,10,7) and normal to the vector n = 9i + 2j…

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Q: Please justify whether these statements are true of false. a. If u and v are vectors in R^3, then…

A: Objects with both magnitude and direction are called vectors. The vector's size is determined by the…

Q: Vectors a' and b are perpendicular to one another. Find k : a'(k², –k, 1), b´ (k, 3, – 2)

A: Scalar product of two vectors

Q: Identify the type of answer that results from each operation (vector or scalar). If the operation is…

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