Define a set of (non-orthogonal) base vectors a = J + K, + K and c 1+J. q = i +4j and r = − (a) Establish their reciprocal vectors and hence express the vectors p = 3i—2j+k, -2i+j+ k in terms of the base vectors a, b and c. (b) Verify that the scalar product p q has the same value, −5, when evaluated using either set of components.

Q: Express the vector = [4] à = vi+ as a a linear combination of ₁ = [] [1] and = [] 02 V2-

A:

Q: Write the vector v = B - 3 8 {[][]}· 8 -2 as a coordinate vector with respect to the basis

A:

Q: Find the vector projection of v = -6i + 10j – konto w = = 2i + j − k (Give your answer using…

A: The given two vectors are  v=-6i+10j-k  and w=2i+j-k

Q: Calculate the triple scalar products w. (vx u) and u (w x v), where u = (7, 2, -1), v = (2, 8, -3),…

A:

Q: (b) 4x Find any values of x such that the vectors 3 and are parallel X-1 to each other.

A:

Q: For the vectors A = ux + 3uy + 5uz, B = 2ux + 4uy + 6uz, and C = 3ux + 4uy + 5uz, show that A × ( B…

A: For the given vectors A,B,C show the given property  If A=a1ux +a2uy+a3uz and B= b1ux+b2uy+b3uz then…

Q: Let u be a vector of length 3 in the direction of the positive y-axis and let v be a vector of…

A: Vector: - The term vector comes from the Latin word vector, which means "carrier." Vectors transport…

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

A:

Q: Find non-zero vectors I and 7 that are both orthogonal to and orthogonal to each other.

A: