The two adjacent sides of a parallelogram are 2\(\hat{i}\)-4\(\hat j\)+5\(\hat k\)and \(\hat{i}\)-2\(\hat j\)-3\(\hat k\). Find the unit vector parallel to its diagonal. Also, find its area.
If either vector \(\vec {a}=\vec{0}\space or\space \vec{b}=\vec{0}\), then \(\vec{a}.\vec{b}=0\).But the converse need not be true.Justify your answer with an example.
Find the position vector of point R which divides the line joining two points P and Q whose position vector is (2\(\vec a\)+\(\vec b\))and(\(\vec a\)-3\(\vec b\))externally in the ratio 1:2. Also, show that P is the midpoint of the line segment RQ.
If \(\vec{a}.\vec{a}=0\) and \(\vec{a}.\vec{b}=0,\)then what can be concluded about the vector \(\vec{b}\)?
Compute the magnitude of the following vectors:\(\overrightarrow{a}\)=\(\hat{i}\)+\(\hat j+\hat k\);\(\overrightarrow{b}\)=2\(\hat{i}\)-7\(\hat{j}\)-3\(\hat{k}\); \(\overrightarrow{c}\)= \(\frac{1}{\sqrt 3}\hat i+\frac{1}{\sqrt 3}\hat j-\frac{1}{\sqrt 3}\hat k\)
Answer the following as true or false. (i)a→and -a→are collinear. (ii)Two collinear vectors are always equal in magnitude. (iii)Two vectors having same magnitude are collinear. (iv)Two collinear vectors having the same magnitude are equal.
In figure, identify the following vectors.
(i)Coinitial (ii)Equal (iii)Collinear but not equal
Classify the following as scalar and vector quantities. (i)Time period (ii)Distance (iii)Force (iv)Velocity (v)Work done
Represent graphically a displacement of 40km,30°east of north.
