Question
Verify (a + a) × (a+ b) = 0⃗ . What can be said about two vectors whose cross product is the zero vector
a x b
= i j k
3 -3 1
-12 12 -4
=
i
( (-3) · (-4) - 1 · 12 ) -
j
( 3 · (-4) - 1 · (-12) ) +
k
( 3 · 12 - (-3) · (-12) ) =
=
i
( 12 - 12 ) -
j
( (-12) - (-12) ) +
k
( 36 - 36 ) =
=
(0 ; 0 ; 0)
2. Relevant equations
have i correctly verified with an example that two vectors whose cross product is the zero vector?
a x b
= i j k
3 -3 1
-12 12 -4
=
i
( (-3) · (-4) - 1 · 12 ) -
j
( 3 · (-4) - 1 · (-12) ) +
k
( 3 · 12 - (-3) · (-12) ) =
=
i
( 12 - 12 ) -
j
( (-12) - (-12) ) +
k
( 36 - 36 ) =
=
(0 ; 0 ; 0)
2. Relevant equations
have i correctly verified with an example that two vectors whose cross product is the zero vector?
Answers
tyler
that looks right....what can be said about them is that they are parallel in space