If θ is the angle between any two vectors \(\vec a\) and \(\vec b\) , then|\(\vec a.\vec b\)|=|\(\vec a \times \vec b\)| when θ is equal to
The value of \(\hat i\).(\(\hat j\)×\(\hat k\))+\(\hat j\).(\(\hat i\times\hat k\))+\(\hat k\).(\(\hat i\times \hat j\)) is
Find the scalar and vector components of the vector with initial point (2,1) and terminal point (-5,7).
Let \(\vec a\) anb \(\vec b\) be two unit vectors and θ is the angle between them.Then,\(\vec a+\vec b\) is a unit vector if
Find the values of x and y so that the vectors \(2 \hat {i} +3\hat{j}\) and \(x \hat {i} +y\hat{j}\) are equal.
If θ is the angle between two vectors \(\vec a\) and \(\vec b\), then \(\vec a.\vec b\)≥0 only when
Prove that (\(\vec a+\vec b\)).(\(\vec a+\vec b\))=|\(\vec a\)|2+|\(\vec b\)|2, if and only if \(\vec a\),\(\vec b\) are perpendicular, given a≠0,b≠0.
If \(α→s\) a nonzero vector of magnitude \('α'\) and \(λ\) a nonzero scalar,then \(λ\vec{α}\) is unit vector if
Show that the vectors \(2\hat{i}-\hat{j}+\hat{k},\hat{i}-3\hat{j}-5\hat{k}\) and \(3\hat{i}-4\hat{j}-4\hat{k}\) from the vertices of a right-angled triangle.
The scalar product of the vector \(\hat i+\hat j+\hat k \) with a unit vector along the sum of vectors \(2\hat i+4\hat j-5 \hat k\) and \(\lambda \hat i+2\hat j+3\hat k\) is equal to one. Find the value of λ.
If the vertices \(A,B,C\) of a triangle \(ABC\) are\((1,2,3),(-1,0,0),(0,1,2)\), respectively,then find \(\angle{ABC}\).[\(\angle{ABC}\) is the triangle between the vectors\( \overrightarrow{BA}\)and \( \overrightarrow{BC}\)].
Show that the direction cosines of a vector equally inclined to the axes OX, OY, and OZ are \(\frac{1}{\sqrt 3}\),\(\frac{1}{\sqrt 3}\),\(\frac{1}{\sqrt 3}\).
