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Question
Points (1,2,3), (9,5,8), (-2,5,6) and (-3,-8,8) are in the same plane.
Points (1,2,3), (9,5,8), (-2,5,6) and (-3,-8,8) are in the same plane.
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Solution
The correct option is B False
For coplanarity of these points
⎛⎜⎝−3−1−8−28−39−15−28−3−2−15−26−3∣∣
∣∣ = ⎛⎜⎝−4−105835−333∣∣
∣∣= −4(9−15)+10(24+15) +5(24+9)= −4×(−6)+10×39+5×33= 24+390+165= 579 ≠0
Since the value of the determinants is not equal to 0. Hence we can say that points are not on the same plane.
For coplanarity of these points
⎛⎜⎝−3−1−8−28−39−15−28−3−2−15−26−3∣∣ ∣∣ = ⎛⎜⎝−4−105835−333∣∣ ∣∣= −4(9−15)+10(24+15) +5(24+9)= −4×(−6)+10×39+5×33= 24+390+165= 579 ≠0
Since the value of the determinants is not equal to 0. Hence we can say that points are not on the same plane.
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