The vector product rule · Short practice

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Recall

Vector products and geometric area — objective 1

Maths4U Original · Short practice

\(a=\left[\begin{matrix}13\\1\\0\end{matrix}\right],\ b=\left[\begin{matrix}0\\1\\14\end{matrix}\right]\). Let \(\displaystyle c=a\times b\).

Find the first component of c.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Vector products and geometric area — objective 1

Maths4U Original · Short practice

\(a=\left[\begin{matrix}14\\1\\0\end{matrix}\right],\ b=\left[\begin{matrix}0\\1\\15\end{matrix}\right]\). Let \(\displaystyle c=a\times b\).

Find the first component of c.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Method

Vector products and geometric area — objective 2

Maths4U Original · Short practice

\(a=\left[\begin{matrix}14\\1\\0\end{matrix}\right],\ b=\left[\begin{matrix}0\\1\\15\end{matrix}\right]\). Let \(\displaystyle c=a\times b\).

Find the second component of c.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Vector products and geometric area — objective 2

Maths4U Original · Short practice

\(a=\left[\begin{matrix}15\\1\\0\end{matrix}\right],\ b=\left[\begin{matrix}0\\1\\16\end{matrix}\right]\). Let \(\displaystyle c=a\times b\).

Find the second component of c.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Apply

Vector products and geometric area — objective 3

Maths4U Original · Short practice

\(a=\left[\begin{matrix}15\\1\\0\end{matrix}\right],\ b=\left[\begin{matrix}0\\1\\16\end{matrix}\right]\). Let \(\displaystyle c=a\times b\).

Find the area of the parallelogram spanned by a and b.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Vector products and geometric area — objective 3

Maths4U Original · Short practice

\(a=\left[\begin{matrix}16\\1\\0\end{matrix}\right],\ b=\left[\begin{matrix}0\\1\\17\end{matrix}\right]\). Let \(\displaystyle c=a\times b\).

Find the area of the parallelogram spanned by a and b.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Check understanding

Vector products and geometric area — objective 4

Maths4U Original · Short practice

\(a=\left[\begin{matrix}16\\1\\0\end{matrix}\right],\ b=\left[\begin{matrix}0\\1\\17\end{matrix}\right]\). Let \(\displaystyle c=a\times b\).

Find the signed scalar triple product (a×b)·(1,0,1).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Vector products and geometric area — objective 4

Maths4U Original · Short practice

\(a=\left[\begin{matrix}17\\1\\0\end{matrix}\right],\ b=\left[\begin{matrix}0\\1\\18\end{matrix}\right]\). Let \(\displaystyle c=a\times b\).

Find the signed scalar triple product (a×b)·(1,0,1).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

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