Answer to Question #106982 in Analytic Geometry for Joshua

Question

Which of this is not true?

a.\\(i \times i=j \times j=k \times k=0\\)

b.\\(\alpha \times \beta = \beta \times \alpha \\)

c.\\(\alpha \times \beta =- \beta \times \alpha \\)

d.\\(\alpha \times \beta \neq \beta \times \alpha \\)

Answer 1

As per the given question

a. $\hat{i} \times \hat{i}=\hat{j} \times \hat{j}=\hat{k} \times \hat{k}=0$

we know that $\hat{i}\times\hat{i}=\sin\theta\hat{n}$

Here angle between i and i, j and j , k and k are 0, hence option A is correct.

b) $\alpha \times \beta = \beta \times \alpha$

we know that

$\alpha\times \beta$ $=-\beta\times \alpha$ Hence option b is false.

c) $-\beta\times \alpha$

From the above we can say that option c is correct.

d)$\alpha \times \beta \neq \beta \times \alpha$

from the option above, we can say that option d is also correct.

Hence option b is incorrect