Please help answer it in detailed and please step by step explanation

Two sides of a parallelogram are given as 1 + 2j - 3k and 5i+j-k. Find area of parallelogram and also find the area of triangle formed by the diagonal of the parallelogram.​

103. B.

53. C.

53. The area of a parallelogram is given by 21× the cross product of its diagonals. So, area =21[(3i^+j^−2k^)×(i^−3j^+4k^)] =21∣∣∣∣∣∣∣∣i^31j^1−3k^−24∣∣∣∣∣∣∣∣ =21∣∣∣∣i^(4−6)−j^(12+2)+k^(−9−1)∣∣∣∣ =21∣∣∣∣(−2i^−14j^−10k^)∣∣∣∣ =1+49+25. =75. Answer verified by Toppr. Practice important Questions. Algebra 1. 2988 Qs.

magnitude and direction

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.