Given:
Shift of 3 units to the left 4 units down.
To find:
The transformation rule.
Solution:
The rule of transformation is
...(i)
Here, a<0 if the figure shifts a units left and a>0 if the figure shifts a units right.
Similarly, b<0 if the figure shifts b units down and b>0 if the figure shifts b units up.
If a transformation represents shift of 3 units to the left 4 units down, then a=-3 and b=-4.
Putting a=-3 and b=-4 (i), we get
Therefore, the correct option is B.
Answer:
23
Step-by-step explanation:
Here is the complete question
Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1, 0, -3), (1, 2, 4), and (5, 1, 0).
Solution
We find the volume of the parallelepiped by making a 3 × 3 column matrix whose columns are the corresponding coordinates of the vertices of the parallelepiped.
So, (1, 0, -3), (1, 2, 4) and (5, 1, 0)
The determinant of A is the volume of the parallelepiped. So,
detA = 1(2 × 0 - 4 × 1) - 1(0 × 0 - (-3) × 1) + 5(0 × 4 - (-3) × 2)
= 1(0 - 4) - 1(0 + 3) + 5(0 + 6)
= 1(-4) - 1(3) + 5(6)
= -4 - 3 + 30
= 23
So the volume of the parallelepiped is 23
