If i + 2j + 3k is parallel to the sum of the | vedclass

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

Question

(B) Let the given vectors be $\vec{a} = 3i + \lambda j + 2k$ and $\vec{b} = -2i + 3j + k$. Their sum is $\vec{s} = \vec{a} + \vec{b} = (3-2)i + (\lamb

Vedclass · Accepted Answer

$-1$

Vedclass · Answer

(B) Let the given vectors be $\vec{a} = 3i + \lambda j + 2k$ and $\vec{b} = -2i + 3j + k$. Their sum is $\vec{s} = \vec{a} + \vec{b} = (3-2)i + (\lambda + 3)j + (2+1)k = i + (\lambda + 3)j + 3k$. It is given that the vector $\vec{v} = i + 2j + 3k$ is parallel to $\vec{s}$. Two vectors $x_1i + y_1j + z_1k$ and $x_2i + y_2j + z_2k$ are parallel if their components are proportional,i.e.,$\frac{x_1}{x_2} = \frac{y_1}{y_2} = \frac{z_1}{z_2}$. Applying this to $\vec{v}$ and $\vec{s}$: $\frac{1}{1} = \frac{2}{\lambda + 3} = \frac{3}{3}$. From $\frac{2}{\lambda + 3} = 1$,we get $\lambda + 3 = 2$,which implies $\lambda = -1$.

If $i + 2j + 3k$ is parallel to the sum of the vectors $3i + \lambda j + 2k$ and $-2i + 3j + k$,then $\lambda = \dots$

Similar Questions

Show that the vector $\hat{i}+\hat{j}+\hat{k}$ is equally inclined to the axes $OX, OY,$ and $OZ$.

In the given figure,which of the vectors are equal?

Classify the following measure as a scalar or a vector:
$30 \, km/hr$

Let $|\vec{a}| = |\vec{b}| = |\vec{a} - \vec{b}| = 1$,then the angle between $\vec{a}$ and $\vec{b}$ is:

If $\vec{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}$ and $\vec{b} = \hat{i} + 2\hat{j} - \hat{k}$,then $\vec{a} + \vec{b} = \dots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module