(a cdot i)i + (a cdot j)j + (a cdot k)k = | vedclass

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

Question

(A) Let the vector $a$ be represented in terms of its components as $a = x i + y j + z k$.Then,the dot product of $a$ with the unit vectors $i, j, k$

Vedclass · Accepted Answer

$a$

Vedclass · Answer

(A) Let the vector $a$ be represented in terms of its components as $a = x i + y j + z k$.Then,the dot product of $a$ with the unit vectors $i, j, k$ are:$a \cdot i = (x i + y j + z k) \cdot i = x$$a \cdot j = (x i + y j + z k) \cdot j = y$$a \cdot k = (x i + y j + z k) \cdot k = z$Substituting these values into the given expression:$(a \cdot i)i + (a \cdot j)j + (a \cdot k)k = x i + y j + z k$Since $x i + y j + z k = a$,the expression simplifies to $a$.

$(a \cdot i)i + (a \cdot j)j + (a \cdot k)k = $

Similar Questions

The position vector of the point which divides the line segment joining the points with position vectors $2a - 3b$ and $3a - 2b$ internally in the ratio $2 : 3$ is:

If $\vec{a}$ is any vector in space,then

Classify the following measure as a scalar or a vector:
$20 \text{ m/s}$ towards north

The projection of the vector $i+j+k$ along the vector $j$ is

Given vectors $\vec{a} = 2 \hat{i} - \hat{j} + 2 \hat{k}$ and $\vec{b} = -\hat{i} + \hat{j} - \hat{k}$. The vector in the direction of $\vec{a} + \vec{b}$ with magnitude $\sqrt{2}$ is . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module