DP Mathematics: Analysis and Approaches Questionbank

Find the distance between $L$ and $\prod _3$.

Show that the three planes do not intersect.

Find a vector equation of $L$, the line of intersection of $\prod _1$ and $\prod _2$.

Verify that the point $\text{P}(1, -2, 0)$ lies on both $\prod _1$ and $\prod _2$.

Boxes of mixed fruit are on sale at a local supermarket.

Box A contains 2 bananas, 3 kiwifruit and 4 melons, and costs $6.58.

Box B contains 5 bananas, 2 kiwifruit and 8 melons and costs $12.32.

Box C contains 5 bananas and 4 kiwifruit and costs $3.00.

Find the cost of each type of fruit.

Find the value of $a$ for which the system of equations does not have a unique solution.

Find the solution of the system of equations when $a=2$.

Three planes have equations:

$2x-y+z=5$

$x+3y-z=4$     , where $a\text{, }b\in \mathbb{R}$.

$3x-5y+az=b$

Find the set of values of $a$ and $b$ such that the three planes have no points of intersection.