WBJEE · Maths · Vector Algebra
If the four points with position vectors \(-2\hat i+\hat j + \hat k, \hat i+\hat j+\hat k,\hat j- \hat k\) and \(\lambda \hat j + \hat k\) are coplanar, then \(\lambda\) is equal to
- A 1
- B 2
- C -1
- D 0
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
If four points \(\left(x_{1}, y_{1}, z_{1}\right),\left(x_{2}, y_{2}, z_{2}\right),\left(x_{3}, y_{3}, z_{3}\right)\) and \(\left(x_{4}, y_{4}, z_{4}\right)\) are coplanar, then…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The minimum value of \(\cos \theta+\sin \theta+\frac{2}{\sin 2 \theta}\)
for \(\theta \in(0, \pi / 2),\) isWBJEE 2015 Hard - If (1, 5) be the midpoint of the segment of a line between the line 5x – y – 4 = 0 and 3x + 4y – 4 = 0, then the equation
of the line will beWBJEE 2024 Easy - The number \((101)^{100}-1\) is divisible byWBJEE 2011 Medium
- If \(u(x)\) and \(v(x)\) are two independent solutions of the differential equation \(\frac{d^{2} y}{d x^{2}}+b \frac{d y}{d x}+c y=0\) then additional solution(s) of the given differential equation is(are)WBJEE 2014 Medium
- If \(p=\left(\begin{array}{cc}\cos \frac{\pi}{4} & -\sin \frac{\pi}{4} \\ \sin \frac{\pi}{4} & \cos \frac{\pi}{4}\end{array}\right)\) and \(X=\left(\begin{array}{c}\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}}\end{array}\right)\). Then,
\(P^{3} X\) is equal toWBJEE 2013 Medium - Let \(f(x)=\max \{x+|x|, x-[x]\}, \quad\) where \(\quad \mid x]\) denotes the greateat integer \(\leq x\). Then, the value of \(\int_{-3}^{3} f(x) d x\) isWBJEE 2014 Easy
More PYQs from WBJEE
- On the set \(R\) of real numbers, the relation \(\rho\) is defined by \(x \rho y,(x, y) \in R\)WBJEE 2018 Easy
- Tangents are drawn to the ellipse \(\frac{x^{2}}{9}+\frac{y^{2}}{5}=1\) at the ends of both latusrectum. The area of the quadrilateral, so formed isWBJEE 2017 Medium
- The correct order of \(\mathrm{O}-\mathrm{O}\) bond length in \(\mathrm{O}_{2}, \mathrm{H}_{2} \mathrm{O}_{2}\) and \(\mathrm{O}_{3}\) isWBJEE 2016 Medium
- Let \(A\) be the point \((0,4)\) in the xy-plane and let \(B\) be the point \((2 t, 0)\). Let \(L\) be the midpoint of \(A B\) and let the perpendicular bisector of \(A B\) meet the \(y\)-axis \(M\). Let \(N\) be the midpoint of LM. Then locus of \(N\) isWBJEE 2023 Medium
- Two monochromatic coherent light beams \(A\) and \(B\) have intensities \(L\) and \(\frac{L}{4},\) respectively. If these beams are superposed, the maximum and minimum intensities will beWBJEE 2017 Easy
- If the potential energy of a hydrogen atom in the first excited state is assumed to be zero, then the total energy of \(n\) \(=\infty\) state is,WBJEE 2023 Medium