If vec{a} + 5vec{b} = vec{c} and vec{a} - 7ve | vedclass

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

Question

(A) Given equations are:$(1)$ $\vec{a} + 5\vec{b} = \vec{c}$$(2)$ $\vec{a} - 7\vec{b} = 2\vec{c}$Subtracting $(2)$ from $(1)$:$(\vec{a} + 5\vec{b}) -

Vedclass · Accepted Answer

$\vec{a}$ and $\vec{c}$ are in the same direction,but $\vec{b}$ and $\vec{c}$ are in opposite directions.

Vedclass · Answer

(A) Given equations are:$(1)$ $\vec{a} + 5\vec{b} = \vec{c}$$(2)$ $\vec{a} - 7\vec{b} = 2\vec{c}$Subtracting $(2)$ from $(1)$:$(\vec{a} + 5\vec{b}) - (\vec{a} - 7\vec{b}) = \vec{c} - 2\vec{c}$$12\vec{b} = -\vec{c}$$\vec{b} = -\frac{1}{12}\vec{c}$This implies $\vec{b}$ and $\vec{c}$ are in opposite directions.Now,substitute $\vec{b} = -\frac{1}{12}\vec{c}$ into $(1)$:$\vec{a} + 5(-\frac{1}{12}\vec{c}) = \vec{c}$$\vec{a} - \frac{5}{12}\vec{c} = \vec{c}$$\vec{a} = \vec{c} + \frac{5}{12}\vec{c} = \frac{17}{12}\vec{c}$Since $\frac{17}{12} > 0$,$\vec{a}$ and $\vec{c}$ are in the same direction.Thus,$\vec{a}$ and $\vec{c}$ are in the same direction,but $\vec{b}$ and $\vec{c}$ are in opposite directions.

If $\vec{a} + 5\vec{b} = \vec{c}$ and $\vec{a} - 7\vec{b} = 2\vec{c}$,then which of the following is true?

Similar Questions

If $a$ and $b$ are two vectors such that $a \cdot b = 0$ and $a \times b = 0$,then:

State whether the following statement is true or false:
Two vectors having the same magnitude are collinear.

If $a, b$ and $c$ are three non-collinear points and $ka + 2b + 3c$ is a point in the plane of $a, b$ and $c$, then $k =$

Let $A, B, C$ be distinct points with position vectors $\hat{i} + \hat{j}$,$\hat{i} - \hat{j}$,and $p\hat{i} - q\hat{j} + r\hat{k}$ respectively. If points $A, B, C$ are collinear,then which of the following can be correct?

$A$ vector $\vec{a}$ has components $2p$ and $1$ with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counter-clockwise sense. If,with respect to the new system,$\vec{a}$ has components $p+1$ and $1$,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module