JEE Mains · Maths · STD 12 - 10. vector algebra
Let three vectors \(\overrightarrow{ a }, \overrightarrow{ b }\) and \(\overrightarrow{ c }\) be such that \(\overrightarrow{ c }\) is coplanar with \(\overrightarrow{ a }\) and \(\overrightarrow{ b }, \overrightarrow{ a } \cdot \overrightarrow{ c }=7\) and \(\overrightarrow{ b }\) is perpendicular to \(\overrightarrow{ c },\) where \(\overrightarrow{ a }=-\hat{ i }+\hat{ j }+\hat{ k }\) and \(\overrightarrow{ b }=2 \hat{ i }+\hat{ k },\) then the value of \(2|\overrightarrow{ a }+\overrightarrow{ b }+\overrightarrow{ c }|^{2}\) is .........
- A \(75\)
- B \(50\)
- C \(80\)
- D \(100\)
Answer & Solution
Correct Answer
(A) \(75\)
Step-by-step Solution
Detailed explanation
Let \(\overrightarrow{ c }=\lambda(\overrightarrow{ b } \times(\overrightarrow{ a } \times \overrightarrow{ b }))\) \(=\lambda((\overrightarrow{ b } \cdot \overrightarrow{ b }) \overrightarrow{ a }-(\overrightarrow{ b } \cdot \overrightarrow{ a }) \overrightarrow{ b })\)…
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
- Let \(a, a r, a r^2, \ldots . . .\). be an infinite \(G.P.\) If \(\sum_{n=0}^{\infty} a^n=57\) and \(\sum_{n=0}^{\infty} a^3 r^{3 n}=9747\), then \(a+18 r\) is equal to :JEE Mains 2024 Hard
- Let \(y = y(x)\) be the solution curve of the differential equation \((1 + \sin x)\dfrac{dy}{dx} + (y+1)\cos x = 0\), \(y(0) = 0\). If the curve \(y = y(x)\) passes through the point \(\left(\alpha, \dfrac{-1}{2}\right)\), then a value of \(\alpha\) is :JEE Mains 2026 Easy
- If the shortest distance between the lines \(\frac{\mathrm{x}-\lambda}{2}=\frac{\mathrm{y}-4}{3}=\frac{\mathrm{z}-3}{4}\) and \(\frac{x-2}{4}=\frac{y-4}{6}=\frac{z-7}{8}\) is \(\frac{13}{\sqrt{29}}\), then a value of \(\lambda\) is :JEE Mains 2024 Hard
- Let \(A\) be a \(3 \times 3\) matrix with \(\operatorname{det}( A )=4\). Let \(R _{ i }\) denote the \(i ^{\text {th }}\) row of \(A\). If a matrix \(B\) is obtained by performing the operation \(R _{2} \rightarrow 2 R _{2}+5 R _{3}\) on \(2 A ,\) then \(\operatorname{det}( B )\) is equal to ...... .JEE Mains 2021 Medium
- If the number of integral terms in the expansion of \(\left(3^{\frac{1}{2}}+5^{\frac{1}{8}}\right)^{\text {n }}\) is exactly \(33,\) then the least value of \(n\) isJEE Mains 2020 Medium
- Suppose for a differentiable function \(h, h(0)=0\), \(\mathrm{h}(1)=1\) and \(\mathrm{h}^{\prime}(0)=\mathrm{h}^{\prime}(1)=2\). If \(\mathrm{g}(\mathrm{x})=\mathrm{h}\left(\mathrm{e}^{\mathrm{x}}\right) \mathrm{e}^{\mathrm{h}(\mathrm{x})}\), then \(g^{\prime}(0)\) is equal to :JEE Mains 2024 Medium
More PYQs from JEE Mains
- The probability of a man hitting a target is \(\frac{2}{5}\). He fires at the target \(k\, times\) (\(k\), a given number). Then the minimum \(k\), so that the probability of hitting the target at least once is more than \(\frac{7}{10}\), isJEE Mains 2013 Hard
- Let \(\mathrm{A}(\alpha, 0)\) and \(\mathrm{B}(0, \beta)\) be the points on the line \(5 x+7 y=50\). Let the point \(P\) divide the line segment \(A B\) internally in the ratio \(7: 3\). Let \(3 x-\) \(25=0\) be a directrix of the ellipse \(E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) and the corresponding focus be \(S\). If from \(S\), the perpendicular on the \(\mathrm{x}\)-axis passes through \(\mathrm{P}\), then the length of the latus rectum of \(\mathrm{E}\) is equal toJEE Mains 2024 Hard
- If the solution of the differential equation \((2 x+3 y-2) d x+(4 x+6 y-7) d y=0, y(0)=3\), is \(\alpha x+\beta y+3 \log _e|2 x+3 y-\gamma|=6\), then \(\alpha+2 \beta+3 \gamma\) is equal toJEE Mains 2024 Hard
- The following system of linear equations \(7 x+6 y-2 z=0\) ; \(3 x+4 y+2 z=0\) ; \({x}-2{y}-6{z}=0,\) hasJEE Mains 2020 Hard
- The area enclosed between the curves \(y=x|x|\) and \(\mathrm{y}=\mathrm{x}-|\mathrm{x}|\) is :JEE Mains 2024 Medium
- Normal of the curve \({x^2} + 2xy - 3{y^2} = 0\) at point \((1,1)\) intersect curve again at which quadrantJEE Mains 2015 Hard