If a,b,c are the p^{th},q^{th},r^{th} terms o | vedclass

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

Question

(D) Let the first term of the $A.P.$ be $A$ and the common difference be $D$. The terms are given by:$a = A + (p - 1)D$$b = A + (q - 1)D$$c = A + (r -

Vedclass · Accepted Answer

$\vec x, \vec y$ are orthogonal vectors

Vedclass · Answer

(D) Let the first term of the $A.P.$ be $A$ and the common difference be $D$. The terms are given by:$a = A + (p - 1)D$$b = A + (q - 1)D$$c = A + (r - 1)D$The dot product $\vec x \cdot \vec y$ is given by:$\vec x \cdot \vec y = (q - r)a + (r - p)b + (p - q)c$Substituting the values of $a, b, c$:$\vec x \cdot \vec y = (q - r)(A + (p - 1)D) + (r - p)(A + (q - 1)D) + (p - q)(A + (r - 1)D)$$= A(q - r + r - p + p - q) + D[(q - r)(p - 1) + (r - p)(q - 1) + (p - q)(r - 1)]$$= A(0) + D[qp - q - rp + r + rq - r - pq + p + pr - p - qr + q]$$= 0 + D[0] = 0$Since the dot product is $0$,the vectors $\vec x$ and $\vec y$ are orthogonal.

If $a$,$b$,$c$ are the $p^{th}$,$q^{th}$,$r^{th}$ terms of an $A.P.$ and $\vec x = (q - r)\hat i + (r - p)\hat j + (p - q)\hat k$ and $\vec y = a\hat i + b\hat j + c\hat k$,then:

Similar Questions

The constant value $(\lambda + \mu)$ for which the lines $\vec{r} = (2\hat{i} + \hat{j} + \hat{k}) + \lambda(\hat{i} - 2\hat{j})$ and $\vec{r} = (\hat{i} + \hat{j} - 3\hat{k}) + \mu(\hat{j} + 2\hat{k})$ intersect each other is equal to (where $\lambda$ and $\mu$ are parameters).

Let the vectors $\vec{a}$ and $\vec{b}$ be such that $|\vec{a}|=3$ and $|\vec{b}|=\frac{\sqrt{2}}{3}$. Then $\vec{a} \times \vec{b}$ is a unit vector if the angle between $\vec{a}$ and $\vec{b}$ is

If $\theta$ is the angle between the unit vectors $a$ and $b$,then $\sin \frac{\theta}{2}$ is equal to

If $a \cdot i = 4$,then $(a \times j) \cdot (2j - 3k) = $

It is given that $a, b, c$ are vectors of lengths $6, 8, 10$ respectively. If $a$ is perpendicular to $(b+c)$, $b$ is perpendicular to $(c+a)$, and $c$ is perpendicular to $(a+b)$, then the length of the vector $a+b+c$ is (in $\sqrt{2}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module