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Show that the four points A, B, C and D with position vectors 4^i+5^j+^k,−^j−^k,3^i+9^j+4^k and 4(−^i+^j+^k) respectively are coplannar. OR The scalar product of the vector →a=^i+^j+^k with a unit vector along the sum of vector →b=2^i+4^j+5^k and →c=λ^i+2^j+3^k is equal to one. Find the value of λ and hence find the unit vector along →b+→c. |
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Answer» Show that the four points A, B, C and D with position vectors 4^i+5^j+^k,−^j−^k,3^i+9^j+4^k and 4(−^i+^j+^k) respectively are coplannar. OR The scalar product of the vector →a=^i+^j+^k with a unit vector along the sum of vector →b=2^i+4^j+5^k and →c=λ^i+2^j+3^k is equal to one. Find the value of λ and hence find the unit vector along →b+→c. |
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