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

Channel:
PW Solutions
Subscribers:
443,000
Published on ● Video Link: https://www.youtube.com/watch?v=IjFym7QcVWc


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
šŸ“²PW App Link - https://bit.ly/YTAI_PWAP
šŸŒPW Website - https://www.pw.live



Other Videos By PW Solutions


2023-06-09If the projection of the vector \( \hat{i}+2 \hat{j}+\hat{k} \) on the sum of the two vectors \(...
2023-06-09Find (i) A vector of magnitude \( \sqrt{6} \) perpendicular to the plane \( A B C \) (ii) Area o...
2023-06-09Consider the non-zero vectors \( \vec{a}, \vec{b}, \vec{c} \) and \( \vec{d} \) such that no thr...
2023-06-09Let \( \vec{a} \) and \( \vec{b} \) be two vectors such that \( |2 \vec{a}+3 \vec{b}|=|3 \vec{a}...
2023-06-09Show that the p.v. of circumcentre of a tetrahedron \( O A B C \) is (where \( O \) is the ori...
2023-06-09Let a vector \( \vec{a} \) be coplanar with vectors \( \vec{b}=2 \hat{i}+\hat{j}+\hat{k} \) and ...
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 \( \vec{a}, \vec{b}, \vec{c} \) be three mutually perpendicular vectors of the same magnitud...
2023-06-09Let \( \vec{a}=\alpha \hat{i}+\hat{j}-\hat{k} \) and \( \vec{b}=2 \hat{i}+\hat{j}-\alpha \hat{k}...
2023-06-09Let \( \vec{a}=\hat{i}-2 \hat{j}+3 \hat{k}, \vec{b}=\hat{i}+\hat{j}+\hat{k} \) and \( \vec{c} \)...
2023-06-09Let \( A B C \) be a triangle such that \( \overrightarrow{B C}=\vec{a}, \overrightarrow{C A}=\v...
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 a vector \( \vec{a} \) has a magnitude 9. Let a vector \( \vec{b} \) be such that for every ...
2023-06-09Let \( \vec{a} \) and \( \vec{b} \) be two vectors such that \( |\vec{a}+\vec{b}|^{2}=|\vec{a}|^...
2023-06-09Let the vectors \( \vec{a}=(1+t) \hat{i}+(1-t) \hat{j}+\hat{k} \), \( \vec{b}=(1+t) \hat{i}+(1-+...
2023-06-09In a quadrilateral \( A B C D \) it is given that \( A B \| C D \) and the diagonals \( A C \) a...
2023-06-09Given four non-zero vectors \( \vec{a}, \vec{b}, \vec{c} \) and \( \vec{d} \). The vectors \( \v...
2023-06-09Find the scalars \( \alpha \) and \( \beta \) if \( \vec{a} \times(\vec{b} \times \vec{c})+(\vec...
2023-06-09Solve the following equation for the vector \( \vec{p} ; \vec{p} \times \vec{a} \) \( +(\vec{p} ...
2023-06-09Let \( \left(\begin{array}{lll}\left(a_{1}-a\right)^{2} & \left(a_{1}-b\right)^{2} & \left(a_{1}...
2023-06-09Let \( \vec{a}=\sqrt{3} \hat{i}-\hat{j} \) and \( \vec{b}=\frac{1}{2} \hat{i}+\frac{\sqrt{3}}{2}...