True or False

Geometry Level 4

State True or False :

Let $\vec{\color{#3D99F6}a} , \vec{\color{#D61F06}b} , \vec{\color{#69047E}c}$ be unit vectors such that $\vec{\color{#3D99F6}a} + \vec{\color{#D61F06}b} + \vec{\color{#69047E}c} = 0$ .
Then, $\vec{\color{#3D99F6}a} \times \vec{\color{#D61F06}b} \ , \ \vec{\color{#D61F06}b} \times \vec{\color{#69047E}c} \ , \ \vec{\color{#69047E}c} \times \vec{\color{#3D99F6}a}$ are mutually perpendicular.

True False Can't say

1 solution

Pulkit Gupta
Nov 27, 2015

Lets solve it by geometrical interpretation.

Since the unit vectors add up to zero, they must be confined to the same plane ( whether it be x - , y -, z - xy -, xz , yz or xyz - ).

Since the cross product of two vectors yield a vector perpendicular to those two, we can infer that cross product of two vectors in the same plane can never give rise to mutually perpendicular vectors.

Hence the statement is false.

True or False

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