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If abcda→,b→,c→,d→ are coplanar vectors, show that abcd(a→×b→)×(c→×d→)=0→ - Mathematics

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प्रश्न

If `vec"a", vec"b", vec"c", vec"d"` are coplanar vectors, show that `(vec"a" xx vec"b") xx (vec"c" xx vec"d") = vec0`

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उत्तर

`vec"a" xx vec"b"` is ⊥r  to `vec"a"` and `vec"b"`

`vec"c" xx vec"d"` is ⊥r  to `vec"c"` and `vec"d"`

Since `vec"a", vec"b", vec"c"` and `vec"d"` are coplanar.

`vec"a" xx vec"b", vec"c" xx vec"d"` are ⊥r to same plane

`vec"a" xx vec"b"` parallel to `vec"c" xx vec"d"`

⇒ `(vec"a" xx vec"b") xx (vec"c" xx vec"d") = vec0`

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Vector Triple Product
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Applications of Vector Algebra - Exercise 6.3 [पृष्ठ २४२]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
अध्याय 6 Applications of Vector Algebra
Exercise 6.3 | Q 6 | पृष्ठ २४२

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