The position vectors of the points \( \mathrm{A} \) and \( \mathrm{B} \) with respect to \( \mat.... VIDEO
The position vectors of the points \( \mathrm{A} \) and \( \mathrm{B} \) with respect to \( \mathrm{O} \) are \( 2 \hat{i}+2 \hat{j}+\hat{k} \) and \( 2 \hat{i}+4 \hat{j}+4 \hat{k} \), then
\( \mathrm{P} \)
\( \frac{1}{2}[(\overrightarrow{O A}) \cdot(\overrightarrow{O B})] \) is
(1) 9
(2) 7
(3) 8
(4) None
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions 2024-01-22 Match the statements/expressions in Column-I with the values given in Column II:
\begin{tabular}.... 2024-01-22 The number of complex numbers \( z \) such that \( (1+i) z \) \( =i|z| \).... 2024-01-22 If a line makes angles \( \alpha, \beta \) and \( \gamma \) with the coordinate axes, then \( \c.... 2024-01-22 Match the following lists.
\begin{tabular}{|c|c|c|c|}
\hline & List-I & & List -II \\
\hline (A).... 2024-01-22 \( \vec{a} \) and \( \vec{c} \) are unit vectors and \( |\vec{b}|=4 \) with \( \vec{a} \times \v.... 2024-01-22 The vectors \( a, b \) and \( c \) are equal in length and taken pairwise, make equal angles. If.... 2024-01-22 Let the unit vectors \( a \) and \( b \) be perpendicular and the unit vector \( c \) be incline.... 2024-01-22 Match the entries of Column-I with those of
Column-II.
\begin{tabular}{|l|l|l|l|}
\hline \multic.... 2024-01-22 If a vector \( \vec{r} \) satisfies the equation \( \vec{r} \times(\hat{i}+2 \hat{j}+\hat{k})=\h.... 2024-01-22 The position vectors of the points \( \mathrm{A} \) and \( \mathrm{B} \) with respect to \( \mat.... 2024-01-22 The position vectors of the points \( \mathrm{A} \) and \( \mathrm{B} \) with respect to \( \mat.... 2024-01-22 The volume of the tetrahedron whose vertices are the points with position vectors \( i-6 j+10 k,.... 2024-01-22 Match the items of Column-I with those in Column II.
\begin{tabular}{|l|l|l|l|}
\hline \multicol.... 2024-01-22 If the vector \( 2 i-3 j+7 k \) is inclined at angles \( \alpha, \beta, \gamma \) with the coord.... 2024-01-22 \( P(0,5,6), Q(1,4,7) . R(2,3,7) \) and \( S(3,4,6) \) are four points in the space. The point f.... 2024-01-22 For non-coplanar vectors \( a, b \) and \( c,|(a \times b) . \mathrm{c}|=|a| \)
\( |b||c| \) hol.... 2024-01-22 The points \( (0,7,10),(-1,6,6) \) and \( (-4,9,6) \) are the vertices of.... 2024-01-22 \( \left(x^{2}+y^{2}\right) d y=x y d x \). If \( y\left(x_{0}\right)=e, y(1)=1 \), then value o.... 2024-01-22 If \( \alpha, \beta, \gamma \) are the angles which a line makes with the coordinate axes, then.... 2024-01-22 \( P(1,1,1) \) and \( Q(\lambda, \lambda, \lambda) \) are two points in the space such that \( P.... 2024-01-22 The vectors \( A B=3 i-2 j+2 k \) and \( B C=-i-2 k \) are the adjacent sides of a parallelogram....