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प्रश्न
If the vectors `hat"i" + hat"j" + hat"k"`, `hat"i" - hat"j" + hat"k"` and `2hat"i" + 3hat"j" + "m"hat"k"` are coplanar, then m = ____________.
पर्याय
3
2
−3
−2
MCQ
रिकाम्या जागा भरा
उत्तर
If the vectors `hat"i" + hat"j" + hat"k"`, `hat"i" - hat"j" + hat"k"` and `2hat"i" + 3hat"j" + "m"hat"k"` are coplanar, then m = 2.
Explanation:
Given vector `hat"i" + hat"j" + hat"k"`, `hat"i" - hat"j" + hat"k"` and `2hat"i" + 3hat"j" + "m"hat"k"` are coplanar
∴ `|(1, 1, 1), (1, -1, 1), (2, 3, "m")|` = 0
1(−m − 3) − 1(m − 2) + 1(3 + 2) = 0
−m − 3 − m + 2 + 5 = 0
2m = 4
m = 2
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