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Vectors and matrices — Question 3

QCAA 2024, Paper 2 · 1 mark

Q3 · 2024 · Technology-activeSimple familiar1 mark

QUESTION 3

Given

\mathbf a=\hat{\mathbf j}+\hat{\mathbf k}

and

\mathbf b=2\hat{\mathbf i}+\hat{\mathbf k}

, determine

\mathbf a\times\mathbf b

.

(A)

\hat{\mathbf i}-2\hat{\mathbf j}-2\hat{\mathbf k}

(B)

\hat{\mathbf i}-2\hat{\mathbf j}+2\hat{\mathbf k}

(C)

\hat{\mathbf i}+2\hat{\mathbf j}-2\hat{\mathbf k}

(D)

\hat{\mathbf i}+2\hat{\mathbf j}+2\hat{\mathbf k}

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer C

1 mark

ANSWER

C

Worked solution

Using

\mathbf a=(0,1,1)

and

\mathbf b=(2,0,1)

,

\mathbf a\times\mathbf b=(1,2,-2)=\hat{\mathbf i}+2\hat{\mathbf j}-2\hat{\mathbf k}

.

Selects option C.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.

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