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प्रश्न
If the line r = `(hat"i" - 2hat"j" + 3hat"k") + lambda(2hat"i" + hat"j" + 2hat"k")` is parallel to the plane `"r" * (3hat"i" - 2hat"j" + "m"hat"k")` = 10, then the value of m is ______.
पर्याय
- 2
3
2
- 3
MCQ
रिकाम्या जागा भरा
उत्तर
If the line r = `(hat"i" - 2hat"j" + 3hat"k") + lambda(2hat"i" + hat"j" + 2hat"k")` is parallel to the plane `"r" * (3hat"i" - 2hat"j" + "m"hat"k")` = 10, then the value of m is -2.
Explanation:
Given line,
r = `(hat"i" - 2hat"j" + 3hat"k") + lambda(2hat"i" + hat"j" + 2hat"k")`
is parallel to plane `"r" * (3hat"i" - 2hat"j" + "m"hat"k")` = 0
We know that, if line r = `"a" + lambda"b"` is parallel to plane r·n = d
Then, b · n = 0
`therefore (2hat"i" + hat"j" + 2hat"k") * (3hat"i" - 2hat"j" + "m"hat"k")` = 0
6 - 2 + 2m = 0.
m = - 2
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Vector Product of Vectors (Cross)
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