If a and b represent two non-collinear vector | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given the equation of a line passing through the points with position vectors $a$ and $b$ is $r = ta + (1-t)b$, where $t$ is a scalar parameter.Re

Vedclass · Accepted Answer

a point on the line joining the points whose position vectors are $a$ and $b$

Vedclass · Answer

(B) Given the equation of a line passing through the points with position vectors $a$ and $b$ is $r = ta + (1-t)b$, where $t$ is a scalar parameter.Rearranging the equation, we get $r - b = t(a - b)$.This implies that the vector $(r - b)$ is collinear with the vector $(a - b)$.Thus, the locus of the point represented by $r$ is the straight line passing through the points represented by vectors $a$ and $b$.When $0 \leq t \leq 1$, the point $r$ lies on the line segment joining the points with position vectors $a$ and $b$.

If $a$ and $b$ represent two non-collinear vectors, the equation $r = ta + (1-t)b$ represents

Similar Questions

Let $u, v, w$ be vectors such that $u + v + w = 0$. If $|u| = 3, |v| = 4,$ and $|w| = 5,$ find the value of $u \cdot v + v \cdot w + w \cdot u$.

Classify the following measure as a scalar or a vector:
$30 \, km/hr$

Let $A$ be the set of vectors $a = (a_1, a_2, a_3)$ satisfying $\left(\sum_{i=1}^3 \frac{a_i}{2^i}\right)^2 = \sum_{i=1}^3 \frac{a_i^2}{2^i}$. Then,

If the magnitudes of $\bar{a}$,$\bar{b}$ and $\bar{a}+\bar{b}$ are respectively $3$,$4$ and $5$,then the magnitude of $\bar{a}-\bar{b}$ is

If the position vectors of the vertices $A, B, C$ of a triangle $ABC$ are $7j + 10k$,$-i + 6j + 6k$,and $-4i + 9j + 6k$ respectively,then the triangle is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module