If \( \vec{a}, \vec{b}, \vec{c} \& \vec{d} \) are the pvs of the points \( \mathrm{A}, \mathrm{B... VIDEO
If \( \vec{a}, \vec{b}, \vec{c} \& \vec{d} \) are the pvs of the points \( \mathrm{A}, \mathrm{B}, \mathrm{C} \& \mathrm{D} \) respectively in three dimensional space \& satisfy the relation \( 3 \vec{a}-2 \vec{b}+\vec{c}-2 \vec{d}=0 \), then :
\( \mathrm{P} \)
(A) A, B, C \& D are coplanar
W
(B) the line joining the points \( \mathrm{B} \& \mathrm{D} \) divides the line joining the point \( \mathrm{A} \& \mathrm{C} \) in the ratio \( 2: 1 \).
(C) the line joining the points A \& C divides the line joining the points B \& D in the ratio \( 1: 1 \)
(D) the four vectors \( \vec{a}, \vec{b}, \vec{c} \& \vec{d} \) are linearly dependent.
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions 2023-02-20 True and False (IV Points \( (3,2),(-2,-3) \) and \( (2,3) \) form a right triangle. 2023-02-20 If the points \( A(1,-2), B(2,3), C(-3,2) \) and \( D(-4,-3) \)
(W) are the vertices of a parall... 2023-02-20 Find the area of a parallelogram \( A B C D \), if three of its
(W) vertices are \( A(2,4), B(2+... 2023-02-20 Two vertices of a triangle are \( (8,-6) \) and \( (-4,6) \). The
(W) area of the triangle is 12... 2023-02-20 If two vertices of an equilateral triangle be \( (0,0) \)
(W) \( (3, \sqrt{3}) \). Find the thir... 2023-02-20 Match the conditions/expressions in Column I with statement in Column II. Normals at \( P, Q, R ... 2023-02-20 Consider three vectors \( \vec{p}=\hat{i}+\hat{j}+\hat{k}, \vec{q}=2 \hat{i}+4 \hat{j}-\hat{k} \... 2023-02-20 If \( \lim _{x \rightarrow 0} \frac{1-\cos \left(1-\cos \frac{x}{2}\right)}{2^{\mathrm{m}} x^{\m... 2023-02-20 Point \( A(-1, y) \) and \( B(5,7) \) lie on a circle with centre
P \( O(2,-3 y) \). Find the va... 2023-02-20 Show that the quadrilateral whose vertices are
W \( (1,3),(2,6),(5,7) \) and \( (4,4) \) is a rh... 2023-02-20 If \( \vec{a}, \vec{b}, \vec{c} \& \vec{d} \) are the pvs of the points \( \mathrm{A}, \mathrm{B... 2023-02-20 A vector of magnitude 10 along the normal to the curve \( 3 x^{2}+8 x y+2 y^{2}-3=0 \) at its po... 2023-02-20 Show that the points \( A(2,-2), B(14,10), C(11,13) \) and
(W) \( D(-1,1) \) are the vertices of... 2023-02-20 If two opposite vertices of a rectangle are \( (-1,3) \) and
W \( (4,0) \). Find the coordinates... 2023-02-20 If \( A(x, y) \) is a point on the line joining the points
E \( B(2,-3) \) and \( C(-4,5) \) and... 2023-02-20 Prove that the points \( A(0,1), B(1,4), C(4,3) \) and \( D(3,0) \)
(W) are the vertices of a sq... 2023-02-20 Show that the points \( (4,2),(7,5) \) and \( (9,7) \) do not form (W) a triangle. 2023-02-20 Find the point on Y-axis, equidistant from two points
(W) \( A(-3,4) \) and \( B(3,6) \) on the ... 2023-02-20 If the distance between the points \( A(1,1) \) and \( B(x, 1) \)
W is 5 units, then find the va... 2023-02-20 Find the distance between the points
(i) \( (-6,7) \) and \( (-1,-5) \)
(ii) \( (-7,-3) \) and \... 2023-02-20 (i) Plot the points \( M(5,-3) \) and \( N(-3,-3) \).
W
(ii) What is the length of \( M N \) ?
(...