Consider the non-zero vectors \( \vec{a}, \vec{b}, \vec{c} \) and \( \vec{d} \) such that no thr... VIDEO
Consider the non-zero vectors \( \vec{a}, \vec{b}, \vec{c} \) and \( \vec{d} \) such that no three of which are coplanar then prove that \( \vec{a}[\vec{b} \vec{c} \vec{d}]+\vec{c}[\vec{a} \vec{b} \vec{d}] \) \( =\vec{b}[\vec{a} \vec{c} \vec{d}]+\vec{d}[\vec{a} \vec{b} \vec{c}] \). Hence prove that if \( \vec{a}, \vec{b}, \vec{c} \) and \( \vec{d} \) represent the position vectors of the vertices of a plane quadrilateral then \( \frac{[\vec{b} \vec{c} \vec{d}]+[\vec{a} \vec{b} \vec{d}]}{[\vec{a} \vec{c} \vec{d}]+[\vec{a} \vec{b} \vec{c}]}=1 \)https://bit.ly/YTAI_PWAP https://www.pw.live
Other Videos By PW Solutions 2023-06-09 Let the vectors \( \vec{a}=(1+t) \hat{i}+(1-t) \hat{j}+\hat{k} \), \( \vec{b}=(1+t) \hat{i}+(1-+... 2023-06-09 Let a vector \( \vec{a} \) has a magnitude 9. Let a vector \( \vec{b} \) be such that for every ... 2023-06-09 Let \( \hat{x}, \hat{y} \) and \( \hat{z} \) and be unit vectors such that \( \hat{x}+\hat{y}+\h... 2023-06-09 Let \( \vec{a} \) and \( \vec{b} \) be two vectors such that \( |\vec{a}+\vec{b}|^{2}=|\vec{a}|^... 2023-06-09 Find
(i) A vector of magnitude \( \sqrt{6} \) perpendicular to the plane \( A B C \)
(ii) Area o... 2023-06-09 In a quadrilateral \( A B C D \) it is given that \( A B \| C D \) and the diagonals \( A C \) a... 2023-06-09 Show that the p.v. of circumcentre of a tetrahedron \( O A B C \) is (where \( O \) is the ori... 2023-06-09 Let \( \vec{a}=3 \hat{i}+\hat{j} \) and \( \vec{b}=\hat{i}+2 \hat{j}+\hat{k} \). Let \( \vec{c} ... 2023-06-09 If the vectors \( \vec{b}, \vec{c}, \vec{d} \) are not coplanar, then prove that the vector \( (... 2023-06-09 Let \( \left(\begin{array}{lll}\left(a_{1}-a\right)^{2} & \left(a_{1}-b\right)^{2} & \left(a_{1}... 2023-06-09 Consider the non-zero vectors \( \vec{a}, \vec{b}, \vec{c} \) and \( \vec{d} \) such that no thr... 2023-06-09 Let \( \vec{a}=\sqrt{3} \hat{i}-\hat{j} \) and \( \vec{b}=\frac{1}{2} \hat{i}+\frac{\sqrt{3}}{2}... 2023-06-09 Given four non-zero vectors \( \vec{a}, \vec{b}, \vec{c} \) and \( \vec{d} \). The vectors \( \v... 2023-06-09 Solve the following equation for the vector \( \vec{p} ; \vec{p} \times \vec{a} \) \( +(\vec{p} ... 2023-06-09 \( O \) is the origin of vectors and \( A \) is a fixed point on the circle of radius \( a \) ... 2023-06-09 Find the scalars \( \alpha \) and \( \beta \) if \( \vec{a} \times(\vec{b} \times \vec{c})+(\vec... 2023-06-09 Consider a plane II: \( \vec{r} \cdot(2 \hat{i}+\hat{j}-\hat{k})=5 \), a line \( L_{1} \) : \( \... 2023-06-09 \( \vec{a}, \vec{b}, \vec{c} \) and \( \vec{d} \) are the position vectors of the points \( A \e... 2023-06-09 Let \( \vec{a}, \vec{b} \) and \( \vec{c} \) be non-coplanar unit vectors, equally inclined to o... 2023-06-09 Prove that:
\[
(\vec{a} \times \vec{b}) \times(\vec{c} \times \vec{d})+(\vec{a} \times \vec{c}) ... 2023-06-09 Given three points on the \( x y \) plane on \( O(0,0), A(1,0) \) and \( B(-1,0) \). Point \( P ...
0