WBJEE · Maths · Vector Algebra
If \(\vec{\alpha}=3 \vec{i}-\vec{k},|\vec{\beta}|=\sqrt{5}\) and \(\vec{\alpha} \cdot \vec{\beta}=3\), then the area of the parallelogram for which \(\vec{\alpha}\) and \(\vec{\beta}\) are adjacent sides is
- A \(\sqrt{17}\)
- B \(\sqrt{14}\)
- C \(\sqrt{7}\)
- D \(\sqrt{41}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{41}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned}|\vec{\alpha} \times \vec{\beta}| & =|\vec{\alpha} \| \vec{\beta}| \sin \theta, \quad \cos \theta=\frac{3}{\sqrt{50}} \\ & =\sqrt{50} \times \frac{\sqrt{41}}{\sqrt{50}}=\sqrt{41}\end{aligned}\)
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
- 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 - The trigonometric equation \(\sin ^{-1} x=2 \sin ^{-1} 2 a\) has a real solution, ifWBJEE 2015 Medium
- A fair six-faced die is rolled 12 times. The probability that each face turns up twice is equal toWBJEE 2014 Hard
- The Rolle's theorem is applicable in the interval \(-1 \leq \mathrm{x} \leq 1\) for the functionWBJEE 2009 Easy
- The equation of the plane through the point \((2,-1,-3)\) and parallel to the lines \(\frac{x-1}{3}=\frac{y+2}{2}=\frac{z}{-4}\) and \(\frac{x}{2}=\frac{y-1}{-3}=\frac{z-2}{2}\) isWBJEE 2020 Medium
- The value of \(\cos 15^{\circ} \cos 7 \frac{1^0}{2} \sin 7 \frac{1^0}{2}\) isWBJEE 2009 Easy
More PYQs from WBJEE
- The value of \(2 \cot ^{-1} \frac{1}{2}-\cot ^{-1} \frac{4}{3}\) isWBJEE 2015 Medium
- The coefficient of \(x^{3}\) in the infinite series expansion of \(\frac{2}{(1-x)(2-x)},\) for \(|x| < 1,\) isWBJEE 2014 Hard
- Angle between \(\mathrm{y}^2=\mathrm{x}\) and \(\mathrm{x}^2=\mathrm{y}\) at the origin isWBJEE 2009 Medium
- The value of the integral \(\int_{-1}^{1}\left\{\frac{x^{2015}}{e^{\mid x \mid}\left(x^{2}+\cos x\right)}+\frac{1}{e^{\mid{x} \mid}}\right\} d x\) is equal toWBJEE 2019 Hard
- Let \(f(x)=a x^{2}+b x+c, g(x)=p x^{2}+q x+r\)
\(\begin{array}{lll}\text { such that } & f(1)=g(1), f(2)=g(2) & \text { and }\end{array}\)
\(f(3)-g(3)=2 .\) Then, \(f(4)-g(4)\) isWBJEE 2012 Easy - The value of \(\frac{\log _3 5 \times \log _{25} 27 \times \log _{49} 7}{\log _{81} 3}\) isWBJEE 2010 Easy