a, b and c are three vectors such that |a|=1, | vedclass

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

Question

(C) Given that, $|a|=1, |b|=2, |c|=3$. Since $b$ and $c$ are perpendicular, we have $b \cdot c = 0$. The projection of $b$ on $a$ is $\frac{a \cdot b}

Vedclass · Accepted Answer

$\sqrt{14}$

Vedclass · Answer

(C) Given that, $|a|=1, |b|=2, |c|=3$. Since $b$ and $c$ are perpendicular, we have $b \cdot c = 0$. The projection of $b$ on $a$ is $\frac{a \cdot b}{|a|}$ and the projection of $c$ on $a$ is $\frac{a \cdot c}{|a|}$. Given that these projections are equal, we have $\frac{a \cdot b}{|a|} = \frac{a \cdot c}{|a|}$, which implies $a \cdot b = a \cdot c$. Now, we calculate $|a-b+c|^2$: $|a-b+c|^2 = |a|^2 + |b|^2 + |c|^2 - 2(a \cdot b) + 2(a \cdot c) - 2(b \cdot c)$. Substituting the known values: $|a-b+c|^2 = (1)^2 + (2)^2 + (3)^2 - 2(a \cdot b) + 2(a \cdot b) - 2(0)$. $|a-b+c|^2 = 1 + 4 + 9 = 14$. Therefore, $|a-b+c| = \sqrt{14}$.

$a, b$ and $c$ are three vectors such that $|a|=1, |b|=2, |c|=3$ and $b, c$ are perpendicular. If the projection of $b$ on $a$ is the same as the projection of $c$ on $a$, then $|a-b+c|$ is equal to

Similar Questions

If $a, b, c$ are unit vectors such that $a + b + c = 0,$ then $a \cdot b + b \cdot c + c \cdot a = $

The orthogonal projection of vector $a$ on vector $b$ is given by:

Find the projection of the vector $\hat{i}+3 \hat{j}+7 \hat{k}$ on the vector $7 \hat{i}-\hat{j}+8 \hat{k}$.

If the area of a parallelogram whose diagonals are represented by vectors $\vec{d_1} = 3 \hat{i} + \lambda \hat{j} + 2 \hat{k}$ and $\vec{d_2} = \hat{i} - 2 \hat{j} + 3 \hat{k}$ is $\frac{\sqrt{117}}{2}$ sq. units,then $\lambda=$

If the projection of $\bar{a}$ on $\bar{b}+\bar{c}$ is twice the projection of $\bar{b}+\bar{c}$ on $\bar{a}$,and if $|\bar{b}|=2 \sqrt{2}$,$|\bar{c}|=4$,and the angle between $\bar{b}$ and $\bar{c}$ is $\frac{\pi}{4}$,then $|\bar{a}|=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module