The position vectors of points A and B referred to an origin O are 4i - 3j - k and -8i + 6j + 5k respectively. If AB meets the z-axis at P, find the ratio AP: PB.

the answer is b

a 90 degree rotation across the the origin followed by a reflection across the x-axis.

step-by-step explanation:

large crystals result from very slow cooling.

evaporation of water: this would produce an evaporite which is a sedimentary rock. like a salt pan in a desert. not possible to have volcanic rocks originate this way.

crystalization in molten earth: slow cooling over time. (hundreds to millions of years)

crystalization at earth's surface: this results in fast cooling. (a few hours to a few months or years)

crystalization from cooling off hot water: that would be a hydrothermal deposit. while associated with volcanics they are not volcanic rocks themselves and usually occur fairly rapidly.