Let vec{b} = -hat{i} + 4hat{j} + 6hat{k} and | vedclass

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

Question

(C) The scalar triple product is defined as $[\vec{a} \ \vec{b} \ \vec{c}] = \vec{a} \cdot (\vec{b} 	imes \vec{c})$.For this value to be maximum,$\ve

Vedclass · Accepted Answer

$\frac{1}{3} (2\hat{i} + 2\hat{j} - \hat{k})$

Vedclass · Answer

(C) The scalar triple product is defined as $[\vec{a} \ \vec{b} \ \vec{c}] = \vec{a} \cdot (\vec{b} 	imes \vec{c})$.For this value to be maximum,$\vec{a}$ must be in the direction of the vector $\vec{b} 	imes \vec{c}$.First,we calculate the cross product $\vec{v} = \vec{b} 	imes \vec{c}$:$\vec{v} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ -1 & 4 & 6 \ 2 & -7 & -10 \end{vmatrix} = \hat{i}(-40 - (-42)) - \hat{j}(10 - 12) + \hat{k}(7 - 8) = 2\hat{i} + 2\hat{j} - \hat{k}$.The magnitude of this vector is $|\vec{v}| = \sqrt{2^2 + 2^2 + (-1)^2} = \sqrt{4 + 4 + 1} = \sqrt{9} = 3$.Since $\vec{a}$ is a unit vector in the direction of $\vec{v}$,we have $\vec{a} = \frac{\vec{v}}{|\vec{v}|} = \frac{2\hat{i} + 2\hat{j} - \hat{k}}{3}$.

Let $\vec{b} = -\hat{i} + 4\hat{j} + 6\hat{k}$ and $\vec{c} = 2\hat{i} - 7\hat{j} - 10\hat{k}$. If $\vec{a}$ is a unit vector and the scalar triple product $[\vec{a} \ \vec{b} \ \vec{c}]$ has the greatest value,then $\vec{a}$ is equal to:

Similar Questions

The lines $\overline{r}=\overline{a}+\lambda(\overline{b} \times \overline{c})$ and $\overline{r}=\overline{c}+\mu(\overline{a} \times \overline{b})$ will intersect if

$A$ unit vector coplanar with $i+j+3k$ and $i+3j+k$ and perpendicular to $i+j+k$ is

Let $\vec{p} = 2\hat{i} + 3\hat{j} + a\hat{k}$,$\vec{q} = b\hat{i} + 5\hat{j} - \hat{k}$,and $\vec{r} = \hat{i} + \hat{j} + 3\hat{k}$. If $\vec{p}, \vec{q}, \vec{r}$ are coplanar and $\vec{p} \cdot \vec{q} = 20$,then the ordered pair $(a, b)$ is:

If $a, b, c$ are three non-coplanar vectors,then $\frac{a \cdot (b \times c)}{c \times a \cdot b} + \frac{b \cdot (a \times c)}{c \cdot (a \times b)} = $

The sum of the distinct real values of $\mu$,for which the vectors $\mu \hat{i} + \hat{j} + \hat{k}$,$\hat{i} + \mu \hat{j} + \hat{k}$,and $\hat{i} + \hat{j} + \mu \hat{k}$ are coplanar,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module