Meaningful Vector Expressions

F f iv.

Meaningful vector expressions. Which of the following are correct meaningful vector expressions. Ii is not meaningful. So abxc is equivalent to asome vector which makes sense. In fact it is called the scalar triple product and this gives the volume of the parallelepiped formed by the three vectors.

The cross product is defined only for two vectors o the expression is meaningless. If not explain why. Au0001x bu0001 c j. A x b c e.

B c the expression is meaningful. A a b c b a b c c a b c d a b c e a b c d f a b c d. I know that div and curl apply to vector fields grad to scalar fields. 661 state whether each expression is meaningful.

So abc is equivalent to asome scalar which does not make sense. Au0001 bu0001 c. A minimum of two vectors are required to perform a dot product. A x b bxc f.

If so state whether it is a vector or a scalar. Ff f i know that i makes sense. A b c. A b x c g.

Which of the following expressions are meaningful. The templated class vectorexpressione is required to be a public base of all classes which model the vector expression concept. It is a vector. So abc is not meaningful.

O the expression is meaningless. Vector projection a b jaj2 a 2 0 1 14 1 2 22 12 42 2i j4k 2 21i 1 21j 4 21k 94 1. If so state whether it is a vector or a scalar. Let the unit vectors a and b be perpendicular and the unit vector c be inclined at o to both a and b.

Au0001 b bu0001 cu0001 l. C vector c a vectorb vector c vector d a vector b vector c vector e a vector b vector. If not explain why. It is a scalar.

The resultant dot product of two vectors is a scalar. So abxc is meaningful. Au0001x bu0001 bu0001x cu0001 i. C vector b a vector b vector.

The resultant dot product of a b is a scalar value. For non zero vectors a b c a bc a b c holds if. State whether each expression is meaningful. A a vectorb vector.

I am confused about grad and curls. O the expression is meaningful. A b x b c ca b cu0001 d. State whether the following expressions are vectors scalars or meaningless.

Au0001x bu0001x cu0001 k. The type of the vector expression. Ab c abc iii. So the dot product is also known as a scalar product.

A bu0001 cu0001 h. Again see page 652 for this.