Vectors 1

Classical Mechanics Level 1

The vector sum of 3 vectors $\vec{A},\vec{B},\vec{C}$ is 0. If $\widehat{i}$ and $\widehat{j}$ are in the direction of $\vec{A}$ and $\vec{B}$ respectively, then:

\vec{C}

should be along

\widehat{j}

\vec{C}

should be in the plane of

\widehat{i}

and

\widehat{j}

\vec{C}

should be along

\widehat{k}

\vec{C}

should be along

\widehat{i}

2 solutions

Kartik Sharma
Oct 25, 2014

Start at the origin and draw a vector, any vector. Start at the head of that vector and draw another vector, any vector. Your final vector should go from the head of the second vector back to the origin. The sum of those three vectors is zero.

Three vectors sum to zero under the condition that they are coplanar (lie in a common plane) and form a triangle. If the vectors are not coplanar, they will not sum to zero.

Another way of looking at it is that the sum is zero if any vector is exactly equal in magnitude and opposite in direction to the vector sum (so-called resultant) of the remaining two.

Ramesh Goenka
Oct 21, 2014

the three sides of a triangle are always contained in a plane.. !! had it been A,B,C,D ... the answer would vary accordingly with the given constraint ..

Vectors 1

2 solutions

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