Question

State whether each expression is meaningful. If not, explain why. If so, state whether it is a vector or a scalar.a. a. (bxc)i. The expression is meaningful. It is a vector. ii. The expression is meaningful. It is a scalar. iii. The expression is meaningless. The cross product is defined only for two vectors. iv. The expression is meaningless. The dot product is defined only for two vectors.b. a x (b.c)i. The expression is meaningful. It is a vector. ii. The expression is meaningful. It is a scalar. iii. The expression is meaningless. The cross product is defined only for two vectors. iv. The expression is meaningless. The dot product is defined only for two vectors. c. a x (bxc)i. The expression is meaningful. It is a vector. ii. The expression is meaningful. It is a scalar. iii. The expression is meaningless. The cross product is defined only for two vectors. iv. The expression is meaningless. The dot product is defined only for two vectors. d. (a.b). ci. The expression is meaningful. It is a vector. ii. The expression is meaningful. It is a scalar. iii. The expression is meaningless. The cross product is defined only for two vectors. iv. The expression is meaningless. The dot product is defined only for two vectors. e. (a.b)x(c.d)i. The expression is meaningful. It is a vector. ii. The expression is meaningful. It is a scalar. iv. The expression is meaningless. The cross product is defined only for two vectors. v. The expression is meaningless. The dot product is defined only for two vectors. f. (axb). (cxd)i. The expression is meaningful. It is a vector. ii. The expression is meaningful. It is a scalar. iii. The expression is meaningless. The cross product is defined only for two vectors. iv. The expression is meaningless. The dot product is defined only for two vectors.

Answer 1

Answer:

ii

iii

i

iv

iii

ii

Step-by-step explanation:

a) For the first vector expression a. (bxc)

Yes, the expression is meaningful because the expression is in form of an associative rule, here we have a dot and a cross, the cross is evaluated first, thereafter the dot and eventually the results gives a scalar. the expression can also be written as a. (bxc) = (a.b) x (a.c)

correct option is (ii)

b) for the expression a x(b.c)

Yes, the expression has no meaning, because a cross product can only be expressed for two terms i.e a cross and then a dot as such it is neither a vector nor a scalar and hence the correct option is (iii)

c) for the expression a x (bxc)

Yes, the expression is meaningful because of the dominance of the cross product which can also be written as a x (bxc) = (axb) x(axc) as such it is a vector, correct option is (i)

d) for the expression a.(b.c)

the expression here has no meaning because the dot product can only be expressed for two term as such it is neither vector nor scalar hence the correct option is (iv)

e) for the expression (a.b)x(c.d)

The expression is meaningless because the cross product is only defined for two terms as such the expression can not be written in another way, it is neither scalar nor vector. the correct option is (iii)

f) for the expression (axb) . (cxd)

the expression here is meaningful because if the cross product terms are evaluated first before the dot product, a unique solution will be gotten which will be in terms of a scalar. correct option is (ii)