The triangle inequality for vectors states:
A$|\vec a + \vec b| = |\vec a| + |\vec b|$
B$|\vec a + \vec b| \le |\vec a| + |\vec b|$
C$|\vec a + \vec b| \ge |\vec a| + |\vec b|$
D$|\vec a + \vec b| = |\vec a| - |\vec b|$
Answer & Solution
Correct answer: B. $|\vec a + \vec b| \le |\vec a| + |\vec b|$
In any triangle, the third side cannot exceed the sum of the other two: $|\vec a + \vec b| \le |\vec a| + |\vec b|$, with equality only when $\vec a$ and $\vec b$ are parallel and same-direction.
Related questions
Vector $PQ$ has magnitude 5 units and is inclined at $150^{\circ}$ to the $x$-axis. In theForces $2i-5j+6k$ and $-i-2j-k$ move a particle from $A(4,-3,-2)$ to $B(6,-1,-3)$. The worPosition vectors $2i-j+k$, $i-3j-5k$ and $3i-4j-4k$ form a triangle with sides $ qrt{41}$,When are two vectors counted as equal?What is the magnitude of the position vector with components 9 and 12?Which two features identify a vector?The work done by a constant force F in displacement d isIf a, b, c are mutually perpendicular unit vectors, the value of a · (b × c) is