If vectors $P, Q$ and $R$ have magnitude $5, 12$ and $13 $ units and $\overrightarrow P + \overrightarrow Q = \overrightarrow R ,$ the angle between $Q$ and $R$ is
${\cos ^{ - 1}}\frac{5}{{12}}$
${\cos ^{ - 1}}\frac{5}{{13}}$
${\cos ^{ - 1}}\frac{{12}}{{13}}$
${\cos ^{ - 1}}\frac{7}{{13}}$
Let $\overrightarrow C = \overrightarrow A + \overrightarrow B$
$(A)$ It is possible to have $| \overrightarrow C | < | \overrightarrow A |$ and $ | \overrightarrow C | < | \overrightarrow B|$
$(B)$ $|\overrightarrow C |$ is always greater than $|\overrightarrow A |$
$(C)$ $|\overrightarrow C |$ may be equal to $|\overrightarrow A | + |\overrightarrow B|$
$(D)$ $|\overrightarrow C |$ is never equal to $|\overrightarrow A | + |\overrightarrow B|$
Which of the above is correct
The position vectors of points $A, B, C$ and $D$ are $\vec A = 3\hat i + 4\hat j + 5\hat k,\,\vec B = 4\hat i + 5\hat j + 6\hat k,\,\vec C = 7\hat i + 9\hat j + 3\hat k$ and $\vec D = 4\hat i + 6\hat j$ then the displacement vectors $\overrightarrow {AB} $ and $\overrightarrow {CD} $ are
The vector that must be added to the vector $\hat i - 3\hat j + 2\hat k$ and $3\hat i + 6\hat j - 7\hat k$ so that the resultant vector is a unit vector along the $y-$axis is
$ABC$ is an equilateral triangle. Length of each side is $a$ and centroid is point $O$. then $\overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}=.......$
Six vectors, $\overrightarrow a$ through $\overrightarrow f$ have the magnitudes and directions indicated in the figure. Which of the following statements is true ?