If vector a , b and c are such that a + b + c =0 and | a |=3, | b… - Vidyadip

Question

If vector $\vec{\text{a}},\vec{\text{b}}\text{ and }\vec{\text{c}}$ are such that $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}=0\text{ and }|\vec{\text{a}}|=3, |\vec{\text{b}}|=5\text{ and }|\vec{\text{c}}|=7$ find the angle between $ \vec{\text{a}}$and $ \vec{\text{b}}$.

✓

Answer

$\vec{\text{a}}+\vec{\text{b}}=-\vec{\text{c}}$
$|\vec{\text{a}}|^{2}+|\vec{\text{b}}|^{2}+2\vec{\text{ a}}\cdot\vec{\text{b}}=|\vec{\text{c}}|^{2}$
$9+25+2\text{ }|\vec{\text{a}}|\text{ }|\vec{\text{b}}|\cos\theta=49$
$30\cos\theta=15\Rightarrow\cos\theta=\frac{1}{2}\Rightarrow\theta=60^{o}=\frac{\pi}{3}.$

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 "5 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 function f(x) is befined as follows: $\text{f(x)}=\begin{cases}\text{x}^2+\text{ax}+\text{b},&0\leq\text{x}<2\\3\text{x}+2,&2\leq\text{x}\leq4\\2\text{ax}+5\text{b},&4<\text{x}\leq8\end{cases}$ if is continuous on [0, 8] find the value of a and b.

The x-intercept of the tangent line to a curve is equal to the ordinate of the point of contact. Find the particular curve through the point (1, 1).

Find the vector equation of the line through the origin which is perpendicular to the plane $\vec{\text{r}}\cdot(\hat{\text{i}}+2\hat{\text{j}}+3\hat{\text{k}})=3$

Differentiate $\text{w.r.t. x}$ the function in Exercise :
$\text{x}^\text{x}+\text{x}^\text{a}+\text{a}^\text{x}+\text{a}^\text{a},$ for some fixed $a > 0$ and $x > 0$

Evaluvate the following intregals
$\int\frac{1}{4+3\tan\text{x}}\ \text{dx}$

Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point $'c\ '$ in the indicated interval as stated by the Lagrange's mean value theorem.
$f(x) = x^3 - 2x^2 - x + 3 on [0, 1]$

A particle moves along the curve $\text{y}=\big(\frac{2}{3}\big)\text{x}^3+1.$ Find the points on the curve at which the y-coordinate is changing twice as fast as the x-coordinate.

Find a point on the curve $y = (x - 3)^2$, where the tangent is parallel to the chord joining the points $(3, 0)$ and $(4, 1).$

A school wants to award its students for the values of Honesty, Regularity and Hard work with a total cash award of Rs. 6,000. Three times the award money for Hard work added to that given for honesty amounts to Rs. 11,000. The award money given for Honesty and Hard work together is double the one given for Regularity. Represent the above situation algebraically and find the award money for each value, using matrix method. Apart from these values, namely, Honesty, Regularity and Hard work, suggest one more value which the school must include for awards.

An experiment succeeds twice as often as it fails. Find the probability that in the next 6 trials there will be at least 4 successes.