Evaluate the product (3a-5b) (2a+7b). - Vidyadip

Question

Evaluate the product $\big(3\vec{a}-5\vec{b})\cdot\big(2\vec{a}+7\vec{b}).$

✓

Answer

$\text{Given:}\ \ \ \ \big(3\vec{a}-5\vec{b}\big).\big(2\vec{a}+7\vec{b}\big)$ $=\big({3\vec{a}\big)}.\big(2\vec{a}\big)+\big(3\vec{a}\big).\big(7\vec{b}\big)-\big(5\vec{b}\big).\big(2\vec{a}\big)-\big(5\vec{b}\big).\big(7\vec{b}\big)$$=6\vec{a}.\vec{a}+21\vec{a}.\vec{b}-10\vec{b}.\vec{a}-35\vec{b}.\vec{b}$
$=6\big|\vec{a}\big|^2+21\vec{a}.\vec{b}-10\vec{a}.\vec{b}-35\Big|\vec{b}\Big|^2$
$=6\big|\vec{a}\big|^2+11\vec{a}.\vec{b}-35\Big|\vec{b}\Big|^2$

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 "2 Marks Questions" 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

The mean of a binomial distribution is $10$ and its standard deviation is $2;$ write the value of $q.$

Differentiate the $\frac{{\cos x}}{{\log x}},x > 0$ w.r.t. x.

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\sqrt{1+\Big(\frac{\text{dy}}{\text{dx}}\Big)^2}=\Big(\text{c}\frac{\text{d}^2\text{y}}{\text{dx}^2}\Big)^{\frac{1}{3}}$

Show that the matrix $A=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right]$ satisfies the equation $A ^2-4 A + I =0$. where $I$ is $2 \times 2$ identity matrix and $O$ is $2 \times 2$ zero matrix. Using this equation, find $A^{-1}$

Find x, y satisfying the matrix equation.
$\begin{bmatrix}\text{x}-\text{y}&2&-2\\4&\text{x}&6\end{bmatrix}+\begin{bmatrix}3&-2&2\\1&0&-1\end{bmatrix}=\begin{bmatrix}6&0&0\\5&2\text{x}+\text{y}&5\end{bmatrix}$

Three numbers are chosen from $1$ to $20.$ Find the probability that they are consecutive.

Symmetric and transitive but not reflexive.

If $w$ is an imaginary cube root of unity, find the value of $\begin{vmatrix}1&\text{w}&\text{w}^2\\\text{w}&\text{w}^2&1\\\text{w}^2&1&\text{w}\end{vmatrix}$

$\text{Find} \frac{\text{dy}}{\text{dx}} \text{at } x = 1, \text{y} = \frac{\pi}{4} \text{if } { \sin}^{2}\text{y} + \cos x\text{y = K}.$

Given a non empty set X, consider P (X) which is the set of all subsets of X.
Define the relation R in P (X) as follows:
For subsets A, B in P (X), ARB if and only if A $\subset$ B. Is R an equivalence relation on P (X)? Justify your answer.