Sample Problem 1.9 Given the vectors A = 8i + 4j - 2k N B = 2j + 6k m C = 3i - 2j+ 4k m calculate the following: (1) A - B; (2) the orthogonal component of B in the direc- tion of C; (3) the angle between A and C; (4) A × B; (5) a unit vector that is perpendicular to both A and B; and (6) A × B.C.

Q: If a = i+ 3j +k and b = i+ 9j +k, find a unit vector with positive first coordinate orthogonal to…

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Q: would the two vectors be (1 1 1 0) and then (0 0 0 1)?

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Q: Find a unit vector that is orthogonal to both u and v for u = and v = .

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Q: Consider the two vectors u = i +3j-k and v=4i+5j-k Find the dot product u. v.

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Q: For a given non-zero vector v in R3 there is a unique unit vector parallel to it. True or false.…

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Q: 2; Find a vector of magnitude 3 in the direction v = (0, 3, –4)

A: The given direction is 0,3,-4.

Q: O Find a unit vector (a vector with length 1) that has the direction of 3 2

A: Given below the detailed solution

Q: A. Give the Cross products of the unit vectors (i, j, k).

A: Understanding of cross product of three vectors are required to under this.

Q: Find the cross product of the vectors ä = and b = .

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Q: Find the unit vector parallel to the sum of the vectors a [2, 4, -5], b = [1, 2, 3]. a.

A: Two given vector are ; a= 2i + 4j - 5k b= 1i+ 2j + 3k Resulting of vector a  & vector b  R= a+ b…

Q: Let P be the point (1, –3, 0) and ū be the vector ī = (-3, 6, 2) %3D • Find the point 1 unit away…

A: Given: The point P=(1,-3,0) and the vector v→=-3,6,2

Q: Find a unit vector parallel to the vector a´. a'= (-2,3,–1)

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Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: If a = i+5j + k and b = i+ 9j +k, find a unit vector with positive first coordinate orthogonal to…

A: We have to find

Q: Find a unit vector in the direction of the given vector

A: Follow the procedure given below.

Q: Find the value of a in the vector v (a, b) if b = 9 and ||ū|| = 15 v is in Quadrant I

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Q: Find the projection of the vector v onto the vector w if v = 2i + j and w = 6i + 3j

A: we have given v and w vectors . We have to find the projection of the vector v onto the vector w

Q: (2x sinh2 + 3y cosh?) dx – 3x cosh dy = 0 |

A: Concept Used: For  y'=f(x, y)   ...(*)If f(hx, hy)=hn f(x, y)Then (*) is homogenous equation of…

Q: Let v be the vector The vector of length 3 in the opposite direction as v is 2 Select one: a. -2 O…

A: Vector v  = (1,2,-2) opposite direction to  given vector can be find as -v (-1,-2,2)

Q: Find a unit vector perpendicular to c = (3, 4, −7) and d = (−1, −1, 3)

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