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Addition of Vectors

Let a=i+2j+...

Question

Let $a = i + 2 j + 3 k$ and $b = 3 i + j$ . Find the unit vector in the direction of $a + b$ .

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Solution

Let
$\begin{matrix} \to a = ˆ i + 2 ˆ j + 3 ˆ k \to b = 3 ˆ i + ˆ j \to a + \to b = ˆ i + 2 ˆ j + 3 ˆ k + 3 ˆ i + ˆ j \to a + \to b = 4 ˆ i + 3 ˆ j + 3 ˆ k S o u n i t v e c t o r i n t h e d i r e c t i o n o f \to a + \to b ∣ ∣ ∣ \to a + \to b ∣ ∣ ∣ = \sqrt{4^{2} + 3^{2} + 3^{2}} = \sqrt{16 + 9 + 9} = \sqrt{34} s o u n i t v e c t o r i n t h e d i r e c t i o n o f \to a + \to b i s = \frac{4}{\sqrt{34}} ˆ i + \frac{3}{\sqrt{34}} ˆ j + \frac{3}{\sqrt{34}} ˆ k \end{matrix}$

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Similar questions

Q. The unit vector in the direction of sum of the vectors

\to A = 2 ˆ i + 4 ˆ j - 7 ˆ k

\to B = 4 ˆ i - 6 ˆ j + 4 ˆ k

Q. Find a unit vector in the direction of the resultant of the vectors

\hat{i} - \hat{j} + 3 \hat{k}, 2 \hat{i} + \hat{j} - 2 \hat{k} and \hat{i} + 2 \hat{j} - 2 \hat{k} .

Q. Find a vector of magnitude

\sqrt{171}

which is perpendicular to both of the vectors

\vec{a} = \hat{i} + 2 \hat{j} - 3 \hat{k}

\vec{b} = 3 \hat{i} - \hat{j} + 2 \hat{k}

Q. Find the value of λ so that the following vectors are coplanar:
(i)

\vec{a} = \hat{i} - \hat{j} + \hat{k}, \vec{b} = 2 \hat{i} + \hat{j} - \hat{k}, \vec{c} = λ \hat{i} - \hat{j} + λ \hat{k}

\vec{a} = 2 \hat{i} - \hat{j} + \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - 3 \hat{k}, \vec{c} = λ \hat{i} + λ \hat{j} + 5 \hat{k}

\vec{a} = \hat{i} + 2 \hat{j} - 3 \hat{k}, \vec{b} = 3 \hat{i} + λ \hat{j} + \hat{k}, \vec{c} = \hat{i} + 2 \hat{j} + 2 \hat{k}

\vec{a} = \hat{i} + 3 \hat{j}, \vec{b} = 5 \hat{k}, \vec{c} = λ \hat{i} - \hat{j}

a = i + 2 j + 3 k, b = - i + 2 j + k,

c = 3 i + j,

r

which is normal to both

a

b

. What is the inclination of

r

c

?

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