Introduction of Product of Two Vectors

If  `veca.veca = 0` and `veca . vecb = 0,` then what can be concluded about the vector `vecb`?

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.

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: 
\[\left| \vec{a} \right| = \left| \vec{b} \right| \Rightarrow \vec{a} = \vec{b}\]

Show that the points A, B, C with position vectors `2hati- hatj + hatk`, `hati - 3hatj - 5hatk` and `3hati - 4hatj - 4hatk` respectively, are the vertices of a right-angled triangle. Hence find the area of the triangle

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.

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

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