cartesian vectors 2
posted by Shaila .
let vector U = (vector u1, vector u2) vector V = (vector v1, vector v2) and vector W = (vector w1, vector w2) Prove each property using Cartesian vectors:
a) (vector U+V)+W = vector U+(v+W)
b) k(vector U+V) = k vector U + k vector V
c) (k+m)vector U = k vector U + m vector U

U+V + W = (u1+v1, u2+v2)+(w1,w2)
= (u1+v1+w1 , u2+v2+w2)
=(u1,u2) + (v1+w1`, v2+w2)
= U + (V+W)
Do the others the same way.
Respond to this Question
Similar Questions

Math  vectors
In the product F(vector)=q(V(vector)xB(vector), take q = 4, V(vector)= 2.0i + 4.0j + 6.0k and F(vector)= 136i 176j + 72k. What then is B(vector) in unitvector notation if Bx = By? 
Mamthematics  Vectors
a) If vector u and vector v are noncollinear vectors show that vector u, vector u cross product vector v and (vector u cross product vector v) cross product vector u are mutually othogonal. b) Verify this property using vectors collinear … 
Physics
Let vector A = 4i^ + 4j^, vector B = 2i^  5j^, and vector F = vector A  5(vector B). a) Write vector F in component form. vector F = ? 
Physics
Let vector A = 4i^ + 4j^, vector B = 2i^  5j^, and vector F = vector A  5(vector B). a) Write vector F in component form. vector F = ? 
Vectors
Explain why it is not possible for Vector a • (Vector b • Vector c) to equal (Vector a • Vector b) • Vector c . (This means that the dot product is not associative.) 
Vectors
Verify using an example that Vector a + (Vector b • Vector c) is not equal to (Vector a + Vector b) • (Vector a +Vector c). (This means that addition does not distribute over the dot product.) Explain the problem that arises. 
Vectors
Verify using a specific example that (Vector a + Vector b) × (Vector a – Vector b) = 2(Vector b×Vector a). Expand to the general case to prove that the result is always true. 
calculus
State whether or not the following statements are true. Justify your reasoning.? 
Vectors
Verify using an example that Vector a + (Vector b • Vector c) is not equal to (Vector a + Vector b) • (Vector a +Vector c). Explain the problem that arises 
Physics
If vector a and b are two non collinear unit vectors and vector a+ vector b=√3 then find the value of ( vector a vector b).(2 vector a+ vector b)