Introduction of Product of Two Vectors

Show that the vectors `2hati - hatj + hatk, hati - 3hatj - 5hatk`  and `3hati - 4hatj - 4hatk` from the vertices of a right angled triangle.

If \[\vec{a,} \vec{b}\] are two vectors, then write the truth value of the following statement: 
 \[\vec{a} = - \vec{b} \Rightarrow \left| \vec{a} \right| = \left| \vec{b} \right|\]

If either vector `veca = vec0`  or `vecb = vec0`, then `veca.vecb = 0`. But the converse need not be true. Justify your answer with an example.

If \[\vec{a,} \vec{b}\] are two vectors, then write the truth value of the following statement: 
\[\left| \vec{a} \right| = \left| \vec{b} \right| \Rightarrow \vec{a} = \vec{b}\]

If \[\vec{a,} \vec{b}\] are two vectors, then write the truth value of the following statement: 
\[|\vec{a}| =  |\vec{b}| \Rightarrow \vec{a}  = ± \vec{b} \]

Find the angle between the vectors `hati-hatj and hatj-hatk`

The two vectors \[\hat{j} + \hat{k}\] and \[3 \hat{i} - \hat{j} + 4 \hat{k}\] represents the sides \[\overrightarrow{AB}\] and \[\overrightarrow{AC}\] respectively of a triangle ABC. Find the length of the median through A.