AP EAMCET · Maths · Vector Algebra
If \(\mathbf{a}\) is collinear with \(\mathbf{b}=3 \hat{i}+6 \hat{j}+6 \hat{k}\) and \(\mathbf{a} \cdot \mathbf{b}=27\), then \(|\mathbf{a}|=\)
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
Let \(\mathbf{a}=x \hat{i}+y \hat{j}+z \hat{k}, \mathbf{b}=3 \hat{i}+6 \hat{j}+6 \hat{k}\) \(\mathbf{a} \cdot \mathbf{b}=27\) According to question, \(\mathbf{a}\) is a collinear with \(\mathbf{b}\), then \(\mathbf{a}=\lambda \mathbf{b}\) ...(i)…
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 points whose position vectors are \(2 \mathbf{i}+3 \mathbf{j}+4 \mathbf{k}, 3 \mathbf{i}+4 \mathbf{j}+2 \mathbf{k}\) and \(4 \mathbf{i}+2 \mathbf{j}+3 \mathbf{k}\) are the vertices ofAP EAMCET 2013 Easy
- The arithmetic mean of five natural numbers is 40 . The largest exceeds the smallest number by 10 . If \(\alpha\) is the maximum possible value for the largest of these 5 numbers, then the number of positive integral divisors of \(\alpha\) isAP EAMCET 2021 Hard
- Three vectors \(\bar{a}, \bar{b}, \bar{c}\) satisfy the condition \(\bar{a}+\bar{b}+\bar{c}=\overline{0}\).
If \(|\bar{a}|=1,|\bar{b}|=3,|\bar{c}|=4\) then \(\bar{a} \cdot \bar{b}+\bar{b} \cdot \bar{c}+\bar{c} \cdot \bar{a}=\)AP EAMCET 2022 Easy - \(\cos ^2(x)+\cos ^2\left(x+\frac{\pi}{3}\right)+\cos ^2\left(x-\frac{\pi}{3}\right)=\)AP EAMCET 2020 Easy
- For is equal toAP EAMCET 2021 Medium
- For a complex number \(Z=a+i b\), let \(\hat{\mathrm{Z}}\) \(=b+i a\). If \(Z_1, Z_2\) are such complex numbers, then \(\widehat{\mathrm{Z}_1 \mathrm{Z}_2}=\)AP EAMCET 2019 Easy
More PYQs from AP EAMCET
- In a \(\triangle \mathrm{ABC}\), if \(\sin ^2 \mathrm{~B}=\sin \mathrm{A}\) and \(2 \cos ^2 \mathrm{~A}=3 \cos ^2 \mathrm{~B}\), then the triangle isAP EAMCET 2025 Medium
- If one root of the equation \(a x^3+b x+c=0\) is twice another root, thenAP EAMCET 2023 Easy
- A magnet of magnetic moment \(M\) is rotated through \(360^{\circ}\) in a magnetic field \(H\), the work done will beAP EAMCET 2020 Easy
- Identify the correct statements:
a) In an atom, the possible maximum number of electrons with \(n=4\) and \(m_s=+\frac{1}{2}\) is 16.
b) There are 4 sub shells associated with \(n=5\)
c) \(\mathrm{n}=2, l=1, \mathrm{~m}_l=0\) and \(\mathrm{m}_{\mathrm{s}}=-\frac{1}{2}\) is a possible set of quantum numbers
d) The number of radial nodes for 3 s orbital is 2AP EAMCET 2017 Medium - If \(a x^2+6 x y+b y^2-10 x+10 y-6=0\) represents a pair of perpendicular lines, then the values of \(|a|\) equalsAP EAMCET 2021 Easy
- Let \(C\) be the centre of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) and \(P\) be a point on it. If the tangent at \(P\) to the hyperbola meets the straight lines \(b x-a y=0\) and \(b x+a y=0\) respectively in \(Q\) and \(R\), then \(C Q . C R=\)AP EAMCET 2017 Medium