Download App

Vector Algebra — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVector Algebra1 Mark
Question
Fill in the blanks.
If $|\vec{\text{a}}\times\vec{\text{b}}|^2+|\vec{\text{a}}\cdot\vec{\text{b}}|^2=144$ and $|\vec{\text{a}}|=4,$ then $|\vec{\text{b}}|^2$ is equal to ________.
✓

Answer

If $|\vec{\text{a}}\times\vec{\text{b}}|^2+|\vec{\text{a}}\cdot\vec{\text{b}}|^2=144$ and $|\vec{\text{a}}|=4,$ then $|\vec{\text{b}}|^2$ is equal to 3.Solution:
$|\vec{\text{a}}\times\vec{\text{b}}|^2+|\vec{\text{a}}\cdot\vec{\text{b}}|^2=144$ $|\vec{\text{a}}|^2|\vec{\text{b}}|^2\sin^2\theta+|\vec{\text{a}}|^2|\vec{\text{b}}|^2\cos^2\theta=144$ $\Rightarrow|\vec{\text{a}}|^2|\vec{\text{b}}|^2=144$ $\Rightarrow|\vec{\text{a}}|^2|\vec{\text{b}}|^2=12$ $\Rightarrow4|\vec{\text{b}}|^2=12$ $\Rightarrow|\vec{\text{b}}|^2=3$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Fill In The Blanks[1 Marks ]" from Vector Algebra→Vector Algebra — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If any vector makes angle $\pi-\alpha, \pi-\beta$ and $\pi-\gamma$ with axes $OX , OY$ and OZ , then the direction cosines of $\overrightarrow{ PO }$ will be ____________ .
→
Fill in the blank.
If A and B are square matrices of the same order, then:
  1. (AB)' = _________.
  2. (kA)' = _________. (k is any scalar)
  3. [k(A - B)]' = _________.
→
Fill in the blank. If $\text{f}(\text{x})=[4-(\text{x}-7)^3],$ then $f^{-1}(x) =........$
→
Fill in the blank.
A matrix which is not a square matrix is called a _________ matrix.
→
Fill in the blanks:
If x, y, z ∈ R, then the value of determinant $\begin{vmatrix}(2^\text{x}+2^{-\text{x}})^2&(2^\text{x}-2^{-\text{x}})^2&1\$3^\text{x}+3^{-\text{x}})^2&(3^\text{x}-3^{-\text{x}})^2&1\$4^\text{x}+4^{-\text{x}})&(4^\text{x}-4^{-\text{x}})^2&1\end{vmatrix}$ is:
→
Fill in the blanks.
A plane passes through the points (2, 0, 0) (0, 3, 0) and (0, 0, 4). The equation of plane is __________.
→
Fill in the blanks.
The number of arbitrary constants in the general solution of a differential equation of order three is ________.
→
If $f(x)=\left\{\begin{array}{c}\frac{x^3-a^3}{x-a}, x \neq a \\ b, x=a\end{array}\right.$, is continuous at $x=a$ then $b=$ _________ .
→
Fill in the blanks.
If the feasible region for a LPP is _________, then the optimal value of the objective function Z = ax + by may or may not exist.
→
The curves $y = 4x^2 + 2x - 8$ and $y = x^3 - x + 13$ touch each other at the point $..........$
→