Let \( A B C \) be a triangle such that \( \overrightarrow{B C}=\vec{a}, \overrightarrow{C A}=\v...

Channel:
Subscribers:
447,000
Published on ● Video Link: https://www.youtube.com/watch?v=prP9IRhrNhA



Duration: 9:19
1 views
0


Let \( A B C \) be a triangle such that \( \overrightarrow{B C}=\vec{a}, \overrightarrow{C A}=\vec{b}, \overrightarrow{A B}=\vec{c} \), \( |\vec{a}|=6 \sqrt{2},|\vec{b}|=2 \sqrt{3} \) and \( \vec{b} \cdot \vec{c}=12 \) Consider the statements:
\( (\mathrm{S} 1):|(\vec{a} \times \vec{b})+(\vec{c} \times \vec{b})|-|\vec{c}|=6(2 \sqrt{2}-1) \)
(S2): \( \angle A C B=\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right) \)
Then
(a) Both (S1) and (S2) are true
(b) Only (S1) is true
(c) Only (S2) is true
(d) Both (S1) and (S2) are false
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live




Other Videos By PW Solutions


2023-06-09A line is drawn from the point \( P(1,1,1) \) and perpendicular to a line with direction ratios ...
2023-06-09The locus of a point which moves in such a way that its distance from the line \( \frac{x}{1}=\f...
2023-06-09The shortest distance between the line \( x=y=z \) and the line \( 2 x+y+z-1=0,3 x+y+2 z-2=0 \) ...
2023-06-09Let \( O \) be the origin and \( \overrightarrow{O A}=2 \hat{i}+2 \hat{j}+\hat{k}, \overrightarr...
2023-06-09A plane cutting the axes in \( P, Q, R \) passes through \( (\alpha-\beta, \beta-\gamma, \gamma-...
2023-06-09Let \( a \) and \( b \) be positive real numbers. Suppose \( \overrightarrow{P Q}=a \hat{i}+b \h...
2023-06-09Let \( \hat{i}, \hat{j} \) and \( \hat{k} \) be the unit vectors along the three positive coordi...
2023-06-09If a variable plane cuts the coordinate axes in \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \...
2023-06-09\( \vec{p}, \vec{q} \), and \( \vec{r} \) are three mutually perpendicular vectors of the same m...
2023-06-09Let \( \vec{u}, \vec{v} \) and \( \vec{w} \) be vectors in three-dimensional space, where \( \ve...
2023-06-09Let \( A B C \) be a triangle such that \( \overrightarrow{B C}=\vec{a}, \overrightarrow{C A}=\v...
2023-06-09A line \( L \) passing through origin is perpendicular to the lines \[ \begin{array}{l} L_{1}:...
2023-06-09A line is perpendicular to \( x+2 y+2 z=0 \) and passes through \( (0,1,0) \). The perpendicular...
2023-06-09Two lines \( \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4} \) and \( \frac{x-3}{1}=\frac{y-k}{2}=z \...
2023-06-09Point \( (\alpha, \beta, \gamma) \) lies on the plane \( x+y+z=2 \). Let \( \vec{a}=\alpha \hat{...
2023-06-09For \( p0 \), a vector \( \vec{v}_{2}=2 \hat{i}+(p+1) \hat{j} \) is obtained by rotating the vec...
2023-06-09Let \( \vec{p}=2 \hat{i}+3 \hat{j}+\hat{k} \) and \( \vec{q}=\hat{i}+2 \hat{j}+\hat{k} \) be two...
2023-06-09Let a vector \( \vec{a} \) be coplanar with vectors \( \vec{b}=2 \hat{i}+\hat{j}+\hat{k} \) and ...
2023-06-09If the projection of the vector \( \hat{i}+2 \hat{j}+\hat{k} \) on the sum of the two vectors \(...
2023-06-09Let \( \vec{a}=2 \hat{i}-\hat{j}+5 \hat{k} \) and \( \vec{b}=\alpha \hat{i}+\beta \hat{j}+2 \hat...
2023-06-09Let \( \vec{a} \) and \( \vec{b} \) be two vectors such that \( |2 \vec{a}+3 \vec{b}|=|3 \vec{a}...