Find \(|\vec{a}\times\vec{b}|\) if \(\vec{a}=\hat{i}-7\hat{j}+7\hat{k}\space and\space \vec{b}=3\hat{i}-2\hat{j}+2\hat{k}.\)
Classify the following measures as scalars and vectors. (i)10kg (ii)2metres north-west (iii)40° (iv)40watt (v)10-19coulomb (vi)20m/s2
Show that the points \(A(1,2,7),B(2,6,3)\),and \(C(3,10,-1)\) are collinear.
Area of a rectangle having vertices \(A,B,C,and \space D\) with position vectors\( -\hat{i}+\frac{1}{2}\hat{j}+4\hat{k},\hat{i}+\frac{1}{2}\hat{j}+4\hat{k},\hat{i}-\frac{1}{2}\hat{j}+4\hat{k}\space and -\hat{i}-\frac{1}{2}\hat{j}+4\hat{k}\) respectively is
Find the area of the triangle with vertices \( A(1,1,2),B(2,3,5),and \space C(1,5,5).\)
A girl walks \(4km\) towards west,then she walk \(3km\) in a direction \(30°\)east of north and stops.Determine the girls displacement from her initial point to departure.
If a unit vector \(\vec{a}\) makes an angles \(\frac{\pi}{3}\) with \( \hat{i}\),\(\frac{\pi}{4}\) with \(\hat{j}\) and an acute angle \(θ\) with \(\hat{k}\) then find \(θ\) and hence,the compounds of \(\vec{a}\).
Find a unit vector perpendicular to each of the vector \(\vec{a}+\vec{b} \space and\space \vec{a}-\vec{b}\),where \(\vec{a}=3\hat{i}+2\vec{j}+2\vec{k}\space and \space \vec{b}=\hat{i}+2\hat{j}-2\hat{k}.\)
If \(\vec{a}=\hat{i}+\hat{j}+\hat{k},\vec{b}=2\hat{i}-\hat{j}+3\hat{k}\) and \(\vec{c}=\hat{i}-2\hat{j}+\hat{k}\),find a unit vector parallel to the vector \(2\vec{a}-\vec{b}+3\vec{c}.\)
Find the value of \(x\) for which\( x(\hat{i}+\hat{j}+\hat{k})\)is a unit vector.
If\( \vec{a}=\vec{b}+\vec{c}\), then is it true that |\(\vec{a}\)|=|\(\vec{b}\)|+|\(\vec{c}\)| ? justify your answer.
Find the scalar components and magnitude of the vector joining the points\( P(x_{1},y_{1},z_{1})and Q(x_{2},y_{2},z_{2}).\)
Write down a unit vector in plane,making an angle of \(30°\)with the positive direction of \(x-axis.\)
Let the vectors \(\vec{a}\) and \(\vec{b}\) be such that |\(\vec{a}\)|\(=3\) and |\(\vec{b}\)|\(=\sqrt{\frac{2}{3}}\) ,then \(\vec{a}\times\vec{b}\) is a unit vector,if the angle between \(\vec{a} \) and \(\vec{b}\) is
If either \(\vec{a}=0\) or \(\vec{b}=0\),then \(\vec{a}\times\vec{b}=0\). Is the converse true? Justify your answer with an example.
Given that \(\vec{a}.\vec{b}=0\) and \(\vec{a}\times\vec{b}=0\).What can you conclude about the vectors \(\vec{a}\) and \(\vec{b}\) ?
Show that\((\vec{a}-\vec{b})\times(\vec{a}+\vec{b})=2(\vec{a}\times \vec{b})\)