u * v =( u1v1, UzV2 , Uz V3 , · Un Vn).

Q: Write the vector a=i−4j as the sum of a vector parallel to b=j+k, and a vector perpendicular to b.

A: Express vector a as sum of two vectors one is parallel to vector b and one is perpendicular to b.…

Q: Calculate [1, 2, 2] x [5, -5, -1] -

A:

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

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

Q: Find the unit vector that has the same direction as the vector v = -i + 2j.

A:

Q: Determine whether the vectors u = and v = are perpendicular.

A: As we know that if the dot product of two vctors is zero then we can say that the vectors are…

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: Find the vector v = PQ. Р3 (1,6, 5) Q = (5, 7, 1)

A: To find vector v=PQ→.

Q: Find the component form of the vector.

A: The graph of the vector:To find: The component form of the vector.

Q: Find the dot product of vectors and .

A:

Q: Find the vector v = PQ. Р- (2, 1,4) Q = (-8.25, -4.25, 8) v =

A:

Q: Consider the vectors: u=(-2,6), v=(-3, –4), w =i+9j, and x=8i-6j.

A:

Q: Determine whether the vectors AB and PQ are equal to each other.

A: Solution of the problem as follows

Q: If vector a= and vector b=, find a · b (the dot product of vector a and vector b).

A:

Q: Find the unit vector Â, B, the dot product À. B, and state whether these 2 vectors are orthogonal,…

A: Given vectors are- A→=3,-2 and B→=2,4 To find the unit vector A^, B^ and dot product A.B Unit vector…

Q: how is C equal to the difference of vectors A and B?

A: Dear user, Please read the question. We need to express Vector A in terms of sum of  B and C.

Q: For the vectors, u=−1,0,5 and v=1,4,−4, calculate projvu and scalvu.

A: Vector projection

Q: Explain why the vector 2u × 3v points in the same direction as the vector u × v.

A: Consider the vectors: u=x1i^+x2j^+x3k^v=y1i^+y2j^+y3k^

Q: Express the dot product of u and v in terms of the components of the vectors.

A: Express the dot product of u and v in terms of the components of the vectors.