Question
#3 help please
Given the vectors P^rightarrow = 3 i^cap + 4 j^cap and Q^vector = 2 i^cap + 2 k^cap, find a vector of unit length perpendicular to both P^vector and Q^vector. Write down the results of all possible cross products between i^cap, j^cap, and k^cap. Prove that A^vector times B^vector = - B^vector times A^vector for any two vectors A^vector and B^vector. Prove that A^vector times A^vector = 0 for any vector A^vector. Prove that the determinant form of the cross product renders the same result as the component form. (a) Draw the forces acting on the ladder shown below if there is no friction on the vertical surface. (b) What is the torque equation for an axis located at the bottom of the ladder? (c) What is the torque equation for an axis located at the top of the ladder? (d) What is the torque equation for an axis located at the point in space
Explanation / Answer
Let the required vector be
v = ai + bj + ck
Now cross product of P and Q = (3i + 4j + 0k) X (2i + 0j + 2k) = 8i - 6j -8k
unit length vector perpendicular to both = 8/sqrt(8^2 + 6^2 + 8^2) i - 6/sqrt(8^2 + 6^2 + 8^2) j - 8/sqrt(8^2 + 6^2 + 8^2) k
unit length vector perpendicular to both = 0.624 i - 0.468j -0.624k
