If a, b, c, d are 4 vectors such that a cdot | vedclass

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

Question

(D) We are given four vectors $a, b, c$, and $d$ such that $a \cdot b = 0$, $|a 	imes c| = |a||c|$, and $|a 	imes d| = |a||d|$.From the conditions $

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(D) We are given four vectors $a, b, c$, and $d$ such that $a \cdot b = 0$, $|a 	imes c| = |a||c|$, and $|a 	imes d| = |a||d|$.From the conditions $|a 	imes c| = |a||c|$ and $|a 	imes d| = |a||d|$, we know that $\sin 	heta = 1$ for the angles between $a, c$ and $a, d$ respectively.This implies that $a \perp c$ and $a \perp d$.Since both $c$ and $d$ are perpendicular to $a$, the vector $(c 	imes d)$ must be parallel to $a$.Therefore, we can write $c 	imes d = \lambda a$ for some scalar constant $\lambda$.Now, we evaluate the scalar triple product $[b c d] = b \cdot (c 	imes d)$.Substituting $c 	imes d = \lambda a$, we get $[b c d] = b \cdot (\lambda a) = \lambda (b \cdot a)$.Since $a \cdot b = 0$, it follows that $b \cdot a = 0$.Thus, $[b c d] = \lambda 	imes 0 = 0$.

If $a, b, c, d$ are $4$ vectors such that $a \cdot b = 0$, $|a \times c| = |a||c|$, and $|a \times d| = |a||d|$, then $[b c d] = $

Similar Questions

$|(a \times b) \cdot c| = |a| |b| |c|$,if

If the vectors $\vec{a}=2 \hat{i}-\hat{j}+\hat{k}$,$\vec{b}=\hat{i}+2 \hat{j}-3 \hat{k}$,and $\vec{c}=3 \hat{i}+p \hat{j}+5 \hat{k}$ are coplanar,then $p=$

If $\vec{a}, \vec{b}, \vec{c}$ are three non-coplanar vectors and $\vec{r}$ is any vector,then $[\vec{b} \, \vec{c} \, \vec{r}] \vec{a} + [\vec{c} \, \vec{a} \, \vec{r}] \vec{b} + [\vec{a} \, \vec{b} \, \vec{r}] \vec{c} = \dots$

If $a, b, c$ are non-negative distinct numbers and $a \hat{\imath}+a \hat{\jmath}+c \hat{k}$,$\hat{\imath}+\hat{k}$ and $c \hat{\imath}+c \hat{\jmath}+b \hat{k}$ are coplanar vectors,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module