WBJEE · Maths · Vector Algebra
The position vectors of the points \(A, B, C\) and \(D\) are \(3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+2 \mathbf{k}, \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(4 \hat{\mathbf{i}}-\hat{\mathbf{j}}-\lambda \hat{\mathbf{k}},\) respectively. If the points \(A, B, C\) and \(D\) lie on a plane, the value of \(\lambda\) is
- A 0
- B 1
- C 2
- D \(-4\)
Answer & Solution
Correct Answer
(D) \(-4\)
Step-by-step Solution
Detailed explanation
The position vectors of the points \(A, B, C\) and \(D\) are \(3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}, 5 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and…
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
- A particle is projected vertically upwards. If it has to stay above the ground for 12 seconds, thenWBJEE 2020 Easy
- If the volume of the parallelopiped with \(\vec{a} \times \vec{b}, \vec{b} \times \vec{c}\) and \(\vec{c} \times \vec{a}\) as coterminous edges is 9 cu. units., then the volume of the parallelopiped with \((\vec{a} \times \vec{b}) \times(\vec{b} \times \vec{c}),(\vec{b} \times \vec{c}) \times(\vec{c} \times \vec{a})\) and \((\vec{c} \times \vec{a}) \times(\vec{a} \times \vec{b})\) as coterminous edges isWBJEE 2023 Medium
- If in a triangle \(A B C, \sin A, \sin B, \sin C\) are in A.P., thenWBJEE 2011 Hard
- On the ellipse \(4 x^{2}+9 y^{2}=1\), the points at which the tangents are parallel to the line \(8 x=9 y,\) areWBJEE 2016 Medium
- Let \(f:[a, b] \rightarrow R\) be such that \(f\) is differentiable in \((a, b)\) is continuous at \(x=a\) and \(x=b\) and moreover \(f(a)=0=f(b)\). ThenWBJEE 2018 Medium
- If \(\mathrm{c}_{0}, \mathrm{c}_{1}, \mathrm{c}_{2}, \ldots \ldots \mathrm{c}{15}\) are the Binomial co-efficients in the expansion of \((1+\mathrm{x})^{15}\), then the value of \(\frac{\mathrm{C}{1}}{\mathrm{c}{0}}+2 \frac{\mathrm{C}{2}}{\mathrm{c}{1}}+3 \frac{\mathrm{c}{3}}{\mathrm{c}{2}}+\ldots \ldots+15 \frac{\mathrm{c}{15}}{\mathrm{c}{14}}\) isWBJEE 2020 Medium
More PYQs from WBJEE
- Let \(A\) be a square matrix of order 3 whose all entries are 1 and let \(I_{3}\) be the identity matrix of order \(3 .\) Then, the matrix \(A-3 I_{3}\) isWBJEE 2019 Easy
- If \(\operatorname{adj} \mathrm{B}=\mathrm{A},|\mathrm{P}|=|\mathrm{Q}|=1\), then \(\operatorname{adj}\left(\mathrm{Q}^{-1} \mathrm{BP}^{-1}\right)=\)WBJEE 2025 Medium
- Two positive charges \(Q\) and \(4 Q\) are placed at points \(A\) and \(B\) respectively, where \(B\) is at a distance \(d\) units to the right of \(A\). The total electric potential due to these charges is minimum at \(P\) on the line through \(A\) and \(B\). What is (are) the distance (s) of \(P\) from \(A ?\)WBJEE 2018 Medium
- The de-Broglie wavelength \((\lambda)\) for electron (e), proton \((p)\) and \(\mathrm{He}^{2+}\) ion \((\alpha)\) are in the following order. (Speed of e, p and \(\alpha\) are the same)WBJEE 2022 Easy
- If \(\sin ^{2} \theta+3 \cos \theta=2,\) then \(\cos ^{3} \theta+\sec ^{3} \theta\) is equal out toWBJEE 2013 Hard
- The area enclosed by \(y=\sqrt{5-x^{2}}\) and
\(y=|x-1|\) isWBJEE 2016 Hard