QCE Vault / Specialist Maths Vectors and matrices — Question 2 QCAA 2025, Paper 2 · 1 mark
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QUESTION 2 Which unit vector product is correct?
(A) i ^ × i ^ = − 1 \hat{\mathbf i}\times\hat{\mathbf i}=-1 i ^ × i ^ = − 1 (B) i ^ × k ^ = 0 \hat{\mathbf i}\times\hat{\mathbf k}=0 i ^ × k ^ = 0 (C) j ^ × i ^ = k ^ \hat{\mathbf j}\times\hat{\mathbf i}=\hat{\mathbf k} j ^ × i ^ = k ^ (D) j ^ × k ^ = i ^ \hat{\mathbf j}\times\hat{\mathbf k}=\hat{\mathbf i} j ^ × k ^ = i ^ WORKED SOLUTION
Answer D 1 mark ANSWER D — j ^ × k ^ = i ^ \hat{\mathbf j}\times\hat{\mathbf k}=\hat{\mathbf i} j ^ × k ^ = i ^ Worked solution
The cyclic unit-vector cross products are i ^ × j ^ = k ^ \hat{\mathbf i}\times\hat{\mathbf j}=\hat{\mathbf k} i ^ × j ^ = k ^ , j ^ × k ^ = i ^ \hat{\mathbf j}\times\hat{\mathbf k}=\hat{\mathbf i} j ^ × k ^ = i ^ and k ^ × i ^ = j ^ \hat{\mathbf k}\times\hat{\mathbf i}=\hat{\mathbf j} k ^ × i ^ = j ^ . Reversing the order changes the sign, and a vector crossed with itself is zero. Worked explanation by QCE Vault; correct option verified against the QCAA answer key.
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