Answer:
3.16 square units
Step-by-step explanation:
Find the area of the triangle with vertices: Q(-5,5,-3), R(-6,8,-4), S(-8,2,-4).
Step 1
We find QR and QS
QR = R - Q
= R(-6,8,-4) - Q(-5,5,-3)
= (-1, 3, -1)
QS = S - Q
= S(-8,2,-4) - Q(-5,5,-3)
= (-3, -3, -1)
Step 2
QR × QS
(-1, 3, -1) × (-3, -3, -1)
Using the formula:
a x b = (a2b3 – a3b2)i + (a3b1 – a1b3)j + (a1b2 – a2b1)k
Where a = (a1, a2, a3)
b = (b1, b2, b3)
QR = a
QS = b
(-1, 3, -1) × (-3, -3, -1)
a x b = (a2b3 – a3b2)i + (a3b1 – a1b3)j + (a1b2 – a2b1)k
= ((3 × -1) – (-1×-3))i + ((-1)×-3) – (-1) × -1)j + (-1 × -3) – (3×-3)k
= (-3 - 3)i + (3 – 1)j + (3 – 9)k
= 0i + 2j - 6k = (0,2,-6)
QR × QS = (0,2,-6)
Area of the triangle = √0² + 2² + 6²/ 2
= √0 + 4 + 36/2
= √40/2
= 6.324555320336759 /2
3.1622776602 square units
Approximately = 3.16 square units
