If the vectors a -2 i - y - z j -5 k - and b - x - y i -3 j - z - x k - are equal x-y- z -

Given: nbsp;a #8594;=2i^ (y+z)j^+5k^ #160;and #160;b #8594;=(x+y)i^+3j^+(z+x)k^ nbsp;are equal Two vectors are equal if and only if their correspo ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Equal Vectors

If the vector...

Question

If the vectors $\vec{a} = 2 \hat{i} - (y + z) \hat{j} + 5 \hat{k} and \vec{b} = (x + y) \hat{i} + 3 \hat{j} + (z + x) \hat{k}$ are equal x+y+z= _________________.

Open in App

Solution

Given: $\vec{a} = 2 \hat{i} - (y + z) \hat{j} + 5 \hat{k} and \vec{b} = (x + y) \hat{i} + 3 \hat{j} + (z + x) \hat{k}$ are equal

Two vectors are equal if and only if their corresponding components are equal.
Thus,

$2 = x + y, - (y + z) = 3, 5 = z + x Now, x + y = 2 . . (1) - y - z = 3 . . (2) z + x = 5 . . (3) Subtracting (1) from (3), we get z - y = 3 . . (4) Adding (2) and (4), we get - 2 y = 6 \Rightarrow y = - 3 Substituting the value of y in (1) and (4), we get x - 3 = 2 \Rightarrow x = 5 and z + 3 = 3 \Rightarrow z = 0 Thus, x + y + z = 5 - 3 + 0 = 2$

Hence, x + y + z = 2.

Suggest Corrections

Similar questions

Q. Value of x and y so that the vectors

2 \to i + 3 \to j

and

x ˆ i + y ˆ j

are equal :

Q. Find the values of x and y so that the vectors

2 ˆ i + 3 ˆ j

and

x ˆ i + y ˆ j

are equal.

(i) If a(y+z) = b(z+x) = c(x+y) and out of a, b, c no two of them are equal then show that,

\frac{y - z}{a (b - c)} = \frac{z - x}{b (c - a)} = \frac{x - y}{c (a - b)}

(ii) If

\frac{x}{3 x - y - z} = \frac{y}{3 y - z - x} = \frac{z}{3 z - x - y}

and

x + y + z \neq 0

then show that the value of each ratio is equal to 1.

(iii) If

\frac{a x + b y}{x + y} = \frac{b x + a z}{x + z} = \frac{a y + b z}{y + z}

and

x + y + z \neq 0

then show that

\frac{a + b}{2}

.

(iv) If

\frac{y + z}{a} = \frac{z + x}{b} = \frac{x + y}{c}

then show that

\frac{x}{b + c - a} = \frac{y}{c + a - b} = \frac{z}{a + b - c}

.

(v) If

\frac{3 x - 5 y}{5 z + 3 y} = \frac{x + 5 z}{y - 5 x} = \frac{y - z}{x - z}

then show that every ratio =

\frac{x}{y}

Q. If

\to x, \to y, \to z

are units vectors such that

\to x + \to y + \to z = \to a

(\to x \times \to y) \times \to z = \to b

\to a \cdot \to x = \frac{3}{2}, \to a \cdot \to y = \frac{7}{4}

and

| \to a | = 2,

then which of the following is FALSE?

Q. If

¯ ¯ ¯ x, ¯ ¯ ¯ y, ¯ ¯ ¯ z

are mutually perpendicular unit vectors and

a^x + a^y + c^z

c^x + c^y + b^z

are coplanar, then

Join BYJU'S Learning Program

If the vectors a→=2i^-(y+z)j^+5k^ and b→=(x+y)i^+3j^+(z+x)k^ are equal x+y+z= _________________.

If the vectors $\vec{a} = 2 \hat{i} - (y + z) \hat{j} + 5 \hat{k} and \vec{b} = (x + y) \hat{i} + 3 \hat{j} + (z + x) \hat{k}$ are equal x+y+z= _________________.