Unit Vector - How to find & Verify Unit Vectors

Q) If the sides 𝐴𝐵 and 𝐴𝐶 of △𝐴𝐵𝐶 are represented by vectors 𝑗+𝑘 and 3𝑖 −𝑗 +4𝑘 then

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Q) Unit vector along (𝐏𝐐) ⃗ where coordinates of P and Q are (2, 1, -1) and (4, 4, -7) is

Let 𝐚 ⃗ 𝐚𝐧𝐝 𝐛 ⃗ be two non-zero vectors. Prove that |𝐚 ⃗×𝐛 ⃗ |≤|𝐚 ⃗ |. |𝐛 ⃗ |

Let 𝐚 ⃗ be any vector such that |𝐚 ⃗ |=𝐚. The |𝐚 ⃗×𝐢 ⃗ |^𝟐+|𝐚 ⃗×𝐣 ⃗ |^𝟐+|𝐚 ⃗×𝐤 ⃗ |^𝟐