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Question

The vectors 2¯i3¯j+4¯¯¯k,¯i2¯j+3¯¯¯k and 3¯i+¯j2¯¯¯k

A
are linearly dependent
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B
are linearly independent
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C
form sides of a triangle
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D
are coplanar
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Solution

The correct option is D are linearly independent
Finding the determinant of the coefficient matrix:
∣ ∣234123312∣ ∣=2(43)+3(29)+4(1+6)=30
Since the determinant is 0, the vectors are linearly independent.

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