AP EAMCET · Maths · Vector Algebra
Find \(|\mathbf{a} \times \mathbf{b}|^2\), if \(|\mathbf{a}|=2,|\mathbf{b}|=3\) and \((\mathbf{a}, \mathbf{b})=\frac{\pi}{6}\)
- A -9
- B 9
- C 3
- D -3
Answer & Solution
Correct Answer
(B) 9
Step-by-step Solution
Detailed explanation
\(|\mathbf{a} \times \mathbf{b}|^2=[|\mathbf{a}||\mathbf{b}| \sin \theta]^2=\left(2 \times 3 \times \frac{1}{2}\right)^2=9\)
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
- Find the maximum distance of the point \(K(10,7)\) from the circle \(x^2+y^2-4 x-2 y-20=0\)AP EAMCET 2020 Medium
- \([x]\) denotes the greatest integer less than or equal to \(x\). If \(\{x\}=x-[x]\) and \(\lim _{x \rightarrow 0^{-}} \frac{\sin ^{-1}(x+[x])}{2-\{x\}}=\theta\), then \(\sin \theta+\cos \theta=\)AP EAMCET 2025 Medium
- The area (in sq. units) of the triangle formed by the tangent and normal to the ellipse \(9 x^2+4 y^2=72\) at the point \((2,3)\) with the \(X\)-axis isAP EAMCET 2025 Medium
- If \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a function defined for all \(x \in \mathbb{R}\) by
\(f(x)=x^3+f^{\prime}(1) x^2+f^{\prime \prime}(2) x-f^{\prime \prime \prime}(3)\) then the area (in sq. units) of the triangle formed by \(\mathrm{X}\)-axis, the tangent and the normal drawn to the curve \(y=f(x)\) at \(x=0\) isAP EAMCET 2018 Medium - The plane \(3 x+4 y+6 z+7=0\) is rotated about the line \(\mathbf{r}=(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})+t(2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}})\) until the plane passes through origin. The equation of the plane in the new position isAP EAMCET 2019 Medium
- If \(f(x)=x \tan ^{-1} x\), then \(\lim _{x \rightarrow 1} \frac{f(x)-f(1)}{x-1}\) equals toAP EAMCET 2014 Medium
More PYQs from AP EAMCET
- Three charges \(+5 q, Q\) and \(-2 q\) are kept along a straight line in the same order such that, \(+5 q\) and \(-2 q\) charges are at a distance of \(\frac{2 r}{3}\) and \(\frac{r}{3}\) from the charge \(Q\) respectively. If the net force on the charge \(-2 q\) is zero, then \(Q\) isAP EAMCET 2022 Easy
- If the cold junction is held at \(0^{\circ} \mathrm{C}\), the same thermo emf \(V\) of a thermocouple varies as \(V=10 \times 10^{-6} t-\frac{1}{40} \times 10^{-6} t^2\), where \(t\) is the temperature of the hot junction in \({ }^{\circ} \mathrm{C}\). The neutral temperature and the maximum value of thermo emf are respectively :AP EAMCET 2006 Medium
- Direction ratios of normal to a plane passing through \((1,0,0)\) and \((0,1,0)\) which makes an angle of \(\frac{\pi}{4}\) with the plane \(x+y-3=0\) areAP EAMCET 2017 Hard
- The equation of the line passing through the point of intersection of lines and and the point isAP EAMCET 2020 Easy
- If the values of \(k\) for which the equation \(x^2+2(k+2) x+\) \(6 \mathrm{k}+7=0\) has equal roots are \(\mathrm{k}_1\) and \(\mathrm{k}_2\), then \(\mathrm{k}_1^2+\mathrm{k}_2^2=\)AP EAMCET 2023 Medium
- \(\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]\) is the dimensional formula of the physical quantityAP EAMCET 2022 Easy